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Copyright 1921 

by 

Paul Wenzel and Maurice Krakow 



MAR 22 1321 
©CLA603781 



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Preface 

TO offer an apology to my readers for producing another work on this 
subject would appear as an afterthought, with an open affection for 
a subject that has been very adequately discussed by numerous other 
authors. However, we all maintain a right to choose our books and 
methods that are best adapted to our individual purposes and should there 
not be sufficient material on the subject to meet our requirements, we could 
not gratify our desires. 

Each author before starting the preliminary work on the subject 
which he desires to discuss, should first consider if the information to be 
conveyed will be of scientific value, if it is collective and has been derived 
from the advanced application of its theoretical principles, that have cul- 
minated from years of experience in the application of the principles of 
perspective, and will assist in the advancement of the art of perspective 
drawing to reach its highest attainments. 

A treatise on the subject of perspective to be of practical value, should 
not be treated solely from the technical standpoint, nor should it be too 
brief and obscured by technicalities that are scarcely intelligible; so that 
it can be only used by the technical student, but in a measure it should be 
so treated that it can also be used by the general reader and used as a text 
book by the technical student. The method of delineation should be simple, 
yet comprehensive, with the exactness of mathematical calculations, with 
the least complications and elementary theories that have no purpose other 
than in the theoretical analysis of its primary principles. It should contain 
numerous examples of problems showing the method of procedure, to aid 
in arriving at a solution for similar problems, also examples of unusual 
conditions that have occurred in the practice of the delineator, or those 
that would come under the head of extreme conditions in perspective. 

I can assure the reader that I have nothing to offer that in a sense 
could be considered as new or a novel method of perspective delineation, 
that I have not otherwise found in my researches, as every method has been 
presented in some form or other to the technical student by other 
authors, and it should not be supposed that there will not be discoveries 
made of methods and principles as portrayed in books by little known and 
forgotten pioneers, which should be considered as the height of attainment 
in perspective delineation for that period. But if the reader will accom- 
pany me he will discover some things that are rather novel, and perhaps 
new to him, inasmuch as he will obtain some points of view from the more 
familiar ground as they will present an unaccompanied aspect. 

In this work I have endeavored to present to my contemporaries a 
method of drawing perspectives by the perspective in plan method and 
the only endorsement that I ask is that they will try it when an opportunity 
occurs. 



CONTENTS 

PAGE 

Preface _ _ 3 

Introduction 5 

Perspective . 7 

The Ground Line „ 9 

The Horizon '. 10 

Vanishing Points 11 

The Picture Plane 13 

The Station Point 14 

Parallel Perspective 16 

Oblique Perspective 22 

The Station Point Method of Perspective Delineation 23 

Perspective Plan by the Station Point Method 28 

Perspectives by the Perspective in Plan Method 30 

The Principles of Perspective _ 37 

The Focal Angle 39 

Designing in Perspective....: _ 41 

Picturesque Perspective 44 



Introduction 

The true origin of perspective drawing will always remain veiled in 
obscurity, all records of the researches made by the Greek Authors 
in their attempt to solve the elementary principles of perspective, 
as used in their theatrical decorations and as referred to in the writings 
of Vitruvius are extant. There was little known about the art of perspec- 
tive drawing before the beginning of the sixteenth century, though the 
works by the earlier authors of that period we know by tradition only. 
The first work of any prominence in the English language is that of Dr. 
Brook Taylor, Linear Perspective (1715), in which perspective is reduced 
to mathematical principles. 

The aim of each author in writing on a technical subject is to present 
it from a different point of view, as he wishes to incorporate a new set of 
principles that he has formulated in his practice, or as a tutor ; not new in 
a sense but the perfecting of a system or a set of principles that have been 
in practice, therefore this work should have no difficulty in finding its 
place among the numerous works by other authors that have labored in 
these regions and have given to us that which can not be obliterated with 
time. 

The principles of Descriptive Geometry founded by Monge in the 
seventeenth century, enabled his contemporaries — the authors of treatises 
on the subject of perspective — to obtain solutions for the difficult problems 
that they had long striven to solve. It might be said without recourse that 
the principles of Descriptive Geometry form the basis of elementary per- 
spective, as we are told by our tutors ; for they declare that it is supreme 
discipline for the mental faculties, as it enables them to cover sheets of 
paper with abstruse and intricate demonstrations pertaining to objects in 
space as projected on two planes at right angles to each other; however, 
I fail to find much affinity between the two ; as only in parallel perspective 
the delineator is working with two planes at right angles to each other, 
the earth's plane and the picture plane, the object rests on the earth's 
plane and the picture plane is parallel to one of its faces. In angular 
perspective, the picture plane forms acute angles with two faces of the 
object and it is perpendicular to the earth's plane ; by a perspective drawing 
we cannot ascertain the exact size of the object from the perspective, as 
they do of a body in space by descriptive geometry. 

In the average treatise on perspective, the elementary principles of 
perspective are elaborately treated, consisting of numerous problems to 
be worked out by the student, if he is not his own tutor ; but the aims of 
the average student do not follow this trend, as problems of this character 
are very difficult to grasp, and it is difficult to ascertain their connection 
with perspective; the expectation of reaching the desired goal seems to 
vanish the horizon, therefore he will quickly seek other sources of informa- 



Perspective Delineation 

tion. The sole aim is to produce a drawing that is a close imitation of the 
edifice in perspective, as the image is conveyed to the mind, without having 
a knowledge of its fundamental principles. This can be likened to all 
students and should not be denied them, even though the results obtained 
are very mediocre. It may be the best — but it is none too good, as it 
certainly will be belittled later by other works of real art, when they have 
satisfied themselves that they can draw a perspective; then afterwards 
learn something of its fundamental principles. For this reason it was 
thought best to eliminate a considerable part of the work in elementary 
perspective and by defining the technical terms used in perspective delinea- 
tion — The Ground Line, Horizon, Vanishing Points, Picture Plane, Station 
Point and the different methods of perspective drawing, giving the reason 
for their uses and the various methods of projection, so as to arrive quickly 
at the real work in perspective delineation, of problems in advanced 
perspective. 

Perspective delineation is a mere matter of projection from a point 
in a designated plane to a point in another plane, which may be located 
back of it, in front, above or below the plane mentioned, and from this 
position a portion of the perspective will be delineated. The various plates 
composing this volume have been drawn with this point of view in mind, 
and as a new principle is to be arrived at, it has been fully demonstrated 
by the methods of projection, leaving nothing of indefinite nature that 
would delay the progress of the student. 



Perspective 

A Mental Concept of the Object is Formed 
as it Appears to the Eye in Perspective. 

Perspective is the art of representing on a plane surface objects in 
their apparent form at various distances from the eye, not as we 
know them to be, but as they appear to the eye in perspective. In 
this respect it differs from a positive or a geometrical illustration and it 
may be called pictorial geometry, which forms the basis of scenic design, 
because it governs the relation of objects by perspective principals. 

The impressions conveyed to the mind through the sense of sight of 
our surroundings, is as it would be presented by a perspective drawing and 
not as it would be shown by a geometrical drawing. The optical con- 
vergence of all parallel horizontal lines may not have made an impression 
on the mind of the casual observer, as they have not made a comprehensive 
study of the art of perspective drawing, or compared a geometrical draw- 
ing with a perspective drawing, in which the difference will be readily 
noticed, whereas the geometrical drawing is likely to be little understood, 
but the perspective needs no explanation. It is a representation of that 
which surrounds us, as the eye readily recognizes the picture as that par- 
ticular view had made a lasting impression on their memory. If we step 
forward or backward or turn about, our surroundings will be seen from a 
different point of view, but their perspective lineaments have not changed. 
All the horizontal lines entering into the composition of the objects that 
surround us, seem to converge to a point of infinity on the horizon. The 
apparent reason for this optical convergence cannot be satisfactorily ex- 
plained or demonstrated, so we will have to allow it to pass without further 
discussion, as it is always present like the elements and the recurrence of 
the seasons, to this optical phenomenon we apply the term perspective. 
If the artist in delineating the objects that enter into the composition of his 
pictures ignored the convergence of the horizontal lineaments that are 
parallel to the horizon, then he would be drawing the objects the size he 
knew them to be and not as they appear to the eye in perspective. 

Perspective can be divided into numerous sub-divisions, but all of 
them would come under one general heading, lineal or angular perspective. 
The only difference between them being the angle of view formed by the 
object with its relation to the picture plane. In angular perspective the 
vertical faces of the object are set to form acute angles with the picture 
plane, the width of these faces will vary according to the angle of view. 
For instance a cube with two equal faces when drawn in perspective at 
an angle of ten degrees, one face will be much narrower than the other, 
as shown on Plate No. 29, but when drawn in perspective at an angle of 
forty-five degrees both faces will be equal ; therefore it will be readily seen 



Perspective Delineation 

how an object with two equal faces, when viewed at various angles of view, 
will appear in perspective. 

The picture plane in parallel perspective is assumed to be parallel 
with one of the faces of the object, in delineating the object one vanish- 
ing point is placed at infinity on the horizon, the perspective is then drawn 
with one system of horizontal lines converging to this vanishing point 
and the other system of horizontal lines intersecting at right angles with 
the vertical. It is maintained by most authors that parallel perspective 
should be used for perspectives of interiors and street scenes, but as this 
method is so limited in its uses it should not be recommended for large 
perpective drawings. 

When delineating a street scene in perspective the necessity of two 
vanishing points for the convergence of the parallel lines will be appre- 
ciated more so than by this description, as the view down the street all the 
parallel lines in that direction seem to converge to a vanishing point, the 
parallel lines running in the opposite direction also converge to a vanishing 
point on the horizon, if we are to draw it as we see it, or as it will appear 
in a photograph. See Plates Nos. 8 and 9. If the street scene is drawn in 
angular perspective, using two vanishing points, the objects would be 
viewed at an angle of ten degrees, which would give approximately the 
same view as that drawn by parallel perspective. By drawing the street 
scene in angular perspective all the difficulties encountered in parallel 
perspective will be overcome, also the appearance of the objects will be 
more agreeable to the eye. For illustrations of parallel and angular per- 
spective see Plates Nos. 1,2, 3, 5, 6, 7, 8, 9. 

The picture plane in oblique perspective forms oblique angles with 
the faces of the object that are to be drawn in perspective. An object that 
leans toward or in the opposite direction from the picture plane will be 
drawn in oblique perspective. A church spire with inclined surfaces, a 
box floating in the water loaded on one side, or any leaning object, or one 
with its vertical faces out of plumb, these inclined faces would form 
oblique angles with the picture plane. Plates Nos. 10 and 11. 

Aerial perspective is the art of representing on a plane surface one of 
the myriad aspects of natural phenomenon, as it is non-scientific in char- 
acter, therefore there are no valid rules for its practice, as experience 
should be the ruling guide of the artist in faithfully portraying the myriad 
aspects presented by nature. 

There are numerous short cuts for obtaining solutions in perspective 
drawing without using measuring points, but finding the perspective length 
of lines by direct projection, by using the orthographic plan, or drawing a 
perspective by using the station point and direct projection. These 
methods are better adapted for the purpose of geometrical demonstrations 
and small perspectives rather than they are for perspectives of any pre- 
tence. The only advantages that can be claimed for these methods are 

8 



Perspective Delineation 

that the working drawings can be used by direct projection in place of 
drawing a perspective in plan. They also have many disadvantages as it 
takes up much more working space, with the subsequent projection of all 
the points on the picture plane often leading to errors, as it is necessary 
to transfer these projected points to the perspective, allowing for a greater 
number of errors. The application of a few primary principles, rather 
than a variety of principles, are the essentials to be sought in mastering 
the art of perspective drawing. 

Accuracy is one of the primary essentials in perspective drawing, as 
there is a possibility of small errors being greatly magnified in the course 
of delineation. When the final drawing is started discrepancies that were 
not corrected at the opportune time are likely to mar the appearance of 
the picture in its entirety. This statement should not be interpreted as 
meaning that all perspective drawings should be made with a hard pencil 
for the sake of accuracy, whereas each line drawn leaves a groove in the 
paper, or that strict principles should be adhered to regardless of the effect 
it may have on the picture ; but in the preliminary part of the work, that 
of laying out the measuring points and the projecting of points in front 
of and back of the picture plane should be carefully executed. To guess at 
the location of a subordinate motive without locating it on the perspective 
plan, then projecting it to the perspective, is likely to become a habit after 
a time, which will often lead to a point in question, the reason for the 
faulty appearance of the motive will be laid to distortion in perspective. 
The term distortion, often used by perspective delineators to cover up a 
multitude of faults in their perspectives, is very often misinterpreted. If 
the perspective is correctly drawn there should be no distortion. To sum 
up what is known as distortion, it is rather a fault of the delineator and 
not one of the sins of perspective. 

The Ground Line 

The term ground line used in perspective delineation is the starting 
point for measuring the vertical heights on the object above or below 
the surface of the earth. The ground line may be located above or 
below the horizon. Inasmuch as the topography of the earth's surface 
varies greatly in different localities, there will be no two conditions that are 
exactly alike ; in some instances the ground line will be a horizontal plane, 
as in others it will be inclined toward the object, or possibly it may drop 
in both directions from the starting point. 

When the height of the ground line has been located above or below 
the horizon, it does not change with the undulations of the topography, 
but the difference in the level of the grade should be measured above or 
below this established point, then the height of all objects will be obtained 
by perspective projection from scale measurements on the vertical line of 
heights. If the plot of ground on which the object stands has an irregular 



Perspective Delineation 

contour, the ground line will converge to a vanishing point, following the 
same direction as the grade line shown on the geometrical elevations ; the 
vanishing point for this line will be located in the vertical plane of the 
vanishing point for that system of parallel horizontal lines that converge 
to a vanishing point on the horizon. 

The vanishing point for all inclined grades can be found by measuring 
the height of the rise in the grade above the starting point, then projecting 
this point to an established vertical line on the object, draw a line from 
the starting point to intersect this point, continuing it to the vertical line 
passing through the aforementioned vanishing point, the intersection of 
these two lines establishes the vanishing point for all horizontal lines that 
are parallel to the grade line shown on the geometrical elevations. If the 
grade line slopes downward instead of rising from the starting point, the 
method of delineation will be the reverse of that described above, the depth 
of the drop in the grade should be measured below the starting point then 
projected to an established point on the object. Plate No. 33. 

Before laying out the ground line for the perspective there are numer- 
ous items that should be taken into consideration, namely, the viewpoint 
of the average observer, or the level of their eyes above the grade, which 
is about four feet six inches to five feet; this is also the horizon. If the 
ground line is placed at a higher level than the aforementioned for a per- 
spective of a tall building, it always gives it the appearance of a photograph 
taken with a wide angle lense, also it is likely that the roofs of the acces- 
sories will appear in the picture ; though there is no valid reason to criticize 
this feature of the perspective delineation, however it is a mere supposition 
that the average person will ever view the edifice from that height ; there- 
fore delineators should consider the viewpoint of the average person when 
they are establishing the level of the ground line, by placing himself at 
the same level as the other creatures that move about on the surface of 
the earth. 

The Horizon 

The horizon to the observer is where the earth and the sky apparently 
meet, it is a neutral line on level with the eye, which retains the 
same position even though the observer has ascended to lofty heights 
above the surface of the earth. Figuratively, there are two horizons, one 
for the observer on the surface of the earth and another for the observer 
at any height above it. The distance on the surface of the earth that the 
eye can see from either location is fixed by certain geometrical principles. 
When the observer's view of the horizon is unobstructed by objects 
on the surface of the earth, it then appears to be a horizontal plane, inas- 
much as the maximum curvature in comparison to its circumference is 
relatively small, therefore it is not necessary to consider this curvature 
when delineating perspectives, as the subsidence from a fixed point in- 

10 



Perspective Delineation 

creases with the square root of the distance, on a comparatively level 
section of ground the surface of the earth will partially disappear at three 
miles and any moving object upon it would be lost sight of at a distance of 
four miles. The prevailing conditions of the atmosphere will at all times 
limit the distance the eye can see on the surface of the earth, also the 
topographic contours of the earth's surface. 

The horizon of the observer that has ascended to lofty heights above 
the surface of the earth, in a balloon that is fixed to the earth or other 
mechanical devices that are propelled through the air, the horizon will 
always be on level with their eyes, the earth's surface then appears like a 
huge saucer or a shallow bowl, the rim of the bowl is the horizon and a 
point directly below the observer is the geometric center of the universe. 
The horizon on the ocean or other large bodies of water is known as the 
visible horizon, inasmuch as there are no permanent objects to obstruct 
the view, as the masts are the first part of the ship to appear on the horizon 
followed by the hull, also the masts are the last portion of the ship to 
disappear below the horizon, conveying the impression that it had sunk 
below the waves or went over the edge, as the curvature of the earth is 
not apparent to the eye, however all moving objects on bodies of water 
appear or disappear in the same manner. 

In bird's-eye view perspectives the horizon will be the dividing line 
between the foreground and the background though the more distant ob- 
jects may be delineated as enveloped in an atmospheric haze, it can hardly 
be said that they are in the background of the picture. The location of 
the horizon can be determined in the studio by holding a horizontal cord or 
pencil on level with the eye. 

In pictures it will often be difficult to determine where the dividing 
line between the foreground and the background occurs, figuratively 
there is no dividing line, as the motives in the background are blended 
into those of the foreground, also the details in the motives are more 
defined as they approach the picture plane. The motives in the back- 
ground that are partially obscured by the atmospheric haze, which lends 
to the picture its aerial perspective, are also back of those in the im- 
mediate foreground, therefore it is a matter for the artist to decide, as 
in a collection of landscape pictures, it is likely that there would be various 
types of foregrounds and backgrounds taken from points of view at dif- 
ferent levels. 

Vanishing Points 

Parallel lines that have their origin at a given point and are paral- 
lel to the horizon, appear to diminish in width as they recede from 
the eye of the observer, seemingly they meet at a point farthest from 
the eye, or at a point of infinity on the horizon. These points for each 
system of parallel lines are called vanishing points which may be located 

11 



Perspective Delineation 

at different levels according to their inclination to the horizontal and the 
vertical planes. The vanishing points for any system of parallel lines, 
also for any angle of view are inseparable from certain geometrical prin- 
ciples of delineation, in so far as the converging horizontal lines, though 
they are infinitely extended they cannot subtend an angle of view of more 
than thirty degrees with the plane of the horizon, nor an arc of a circle 
of more than one-hundred and eighty degres, or a semi-circle of which 
the horizon will be the base. 

The vanishing points for any system of parallel lines, may be found 
by allowing the eye to follow the direction of their convergence to a vanish- 
ing point, in whatever plane they may be located. When the vanishing 
point for that system of parallel lines has been found, a horizontal chord 
or pencil held on level with the eye will give the position of the horizon, 
it will then be a simple matter to ascertain in what plane they are located. 
A system of lines coinciding to the raking lines of eaves, gables and 
pediments when extended to infinity, the vanishing point will be found in 
the vertical plane of the vanishing point, for that system of horizontal lines 
that converge to a vanishing point on the horizon. The convergence of that 
system of parallel lines may not be perceptible as those in a horizontal 
plane, as motives of this character are used sparingly in architectural 
composition, however, in a series of gables or pediments the convergence 
of the receding lines in the composition of the motives will be very 
noticeable. 

The vanishing points for a system of lines in a vertical plane when 
infinitely extended will be found in the apex of the object. Parallel lines 
coinciding to those of a church spire, smoke stacks and the entasis of 
columns, have a vanishing point in a vertical plane passing through the 
center of the base terminating at the apex. 

It is not essential that vanishing points be obtained for each system 
of parallel line of the various motives in the composition as in many 
instances it will not be necessary; but the object that is nearest the ob- 
server, should be carefully delineated by finding the vanishing points for 
each system of parallel lines that enter into its composition. In photo- 
graphs this convergence is very perceptible, as the distance from the eye 
increases the magnitude of the motives entering into the composition 
diminish in size, as their remoteness becomes manifest, inasmuch as the 
horizon may be obscured by an atmospheric haze that renders distances 
indefinite ; when this haze becomes more dense all the details in the com- 
position of the motives will be lost sight of, then they will be silhouetted 
with the sky as a background, their mass will be the only part of them 
that is visible, this diminution is due to the angle subtended by the point 
of view. 

When drawing perspectives of tall buildings there will be reason 
to think that the system of vertical lines in the composition should con- 

12 



Perspective Delineation 

verge to a vanishing point in space, however, if there is any convergence 
to this system of vertical lines it is not perceptible. If the viewpoint 
selected for a tall building is such that the building can be seen in its 
entirety and a plumb-line is held up to coincide with its vertical wall 
surfaces at one corner with space as its background, it will be readily 
seen that there is no convergence to the vertical lines as compared to those 
in the horizontal plane. In no instance would this convergence be per- 
ceptible, unless the vertical wall surfaces were designed to have an entasis 
like that of a column. Where the vertical wall surfaces are battered or 
stepped back as they are on some Gothic Church Towers in a decorative 
manner, the vanishing point for the battered or stepped wall surface 
will be found in the apex of the motive coinciding with the center line 
that passes through the base. The convergence of the vertical lines can 
be readily noticed in photographs taken with kodak lense tilted at an 
oblique angle to the vertical plane without using a wide angle lense, though 
the wide angle lense will not totally obviate this distortion in the vertical 
lines of the object, as there is a tendency for that system of lines to con- 
verge to a vanishing point in space. Photographs that show an inclination 
to the vertical lines are distorted, this distortion can be imitated in perspec- 
tive by using conguate vanishing points, which are in pairs, the whole 
group will then be called tri-conguate, as this method of perspective de- 
lineation is of no practical value it will not be further considered. 

Parallel lines other than those parallel to the horizon have their 
convergence point in the place of their origin. A beam of light coming 
through an aperture in the clouds, which illuminates a portion of the earths 
surface, is the same width at each end, although the boundary lines of the 
beam seem to converge to a vanishing point farthest from the eye. 

There are numerous examples among buildings where there will be 
no convergence to certain systems of parallel lines in the composition of 
the motives, the ground plan of these buildings is either half of a regular 
or an irregular polygon. The perspective of a building with an irregular 
ground plan would show three of the geometrical elevations in place of 
two as in the ordinary perspective. Each system of parallel horizontal 
lines on the side elevations when drawn in perspective will have a conver- 
gence point on the horizon, the same systems of horizontal lines on the 
third elevation, or the elevation nearest the station point, will connect the 
terminating horizontal lines of the other two elevations without a con- 
vergence point. Plates Nos. 21 and 22. 

The Picture Plane 

THE term picture plane used in perspective delineation has a cor- 
responding meaning to the term plane used in geometrical demon- 
strations, inasmuch as it is assumed to be an imaginary, transparent, 
vertical plane, arbitrarily placed between the observer and the object 

13 



Perspective Delineation 

viewed; it can be defined as a surface real or imaginary, parallel to the 
horizon and perpendicular to the surface of the earth, a section of which 
will be a straight line. 

Perspective is the representation of objects on the picture plane as 
they appear to the observer when viewed from a station point. The 
picture plane as an accessory to the art of perspective drawing serves 
numerous purposes, in so far as it establishes the location of the principal 
motives in the picture, with their relation to the subordinate, also those 
that are located in front of this plane as well as those that are back of it. 

The picture plane of the artist serves a slightly different purpose 
than that used in perspective delineation, inasmuch as it is arbitarily 
placed between the station point and the objects viewed, in this position 
there would be a foreshortening of the objects in both dimensions, in 
their height and their length. In most pictures the principal motive 
in the composition is a short distance back of the picture plane, when 
the landscape pictures by the artist are compared with the architectural 
perspectives by the delineator, they will always appear slightly different 
on account of the location of the picture plane. The picture plane for the 
delineation of architectural perspectives is set to form acute angles with 
two faces of the object or is parallel with one of its faces, in this position 
it will cut through the portions of the object that project beyond the 
vertical wall surfaces, also through the projecting wings and accessories. 
The picture plane in the camera or the ground glass, is back of the station 
point, then the reflected image is inverted. The picture plane is back of 
the object when the projected image is larger than the object, as it often 
does in the delineation of the accessories for an architectural perspective. 

A window will serve the purpose of a picture plane when the observer 
is stationed in a room, viewing a group of objects or a landscape out of 
doors, the picture is then represented on the picture plane. When the 
observer approaches the window the angle of vision from which the 
objects are viewed will be increased and more of the surroundings will be 
included in the composition, by stepping back from the window the angle 
of vision is decreased, then the view of the objects is taken from a greater 
distance, in so far as the sides of the window cut off a portion of the sur- 
roundings, eventually one object will fill the entire space between the sides 
of the window. 

The Station Point 

THE pictures of all objects drawn in perspective are viewed from a 
station point, the station point may be located on the surface of 
the earth or it may be taken from any point above or below this 
level, each situation will give a different view of the objects. The selec- 
tion of a station point is a matter that requires more than a casual con- 
sideration, as any change in the point of view will have a reaction on the 

14 



Perspective Delineation 

picture in its intirety; if the picture to be delineated consists of one prin- 
cipal object with its accessories, it is essential that the observer should 
be far enough away from it so as to see its topmost members without 
throwing the head back, so that only a portion of the object can be seen 
at one time. If the object can not be seen in its entirety from this point 
of view, the observer should step further back as any change in the location 
of the station point will suffice for correcting the defects of the first 
selected station point. 

The location of the station point establishes the position of all of 
the principal points for the delineation of perspectives, in so far as it 
fixes the position of the vanishing points, the measuring points for the 
perspective in plan and the depth of the ground line below the horizon 
for the perspective. The station point should not be located too close to 
the object as the perspective will then appear distorted, nor at too great 
a distance from it as there will then be a maximum convergence to the 
parallel horizontal lines, also at a great distance from the object many of 
the principal details will be obscured by the atmospheric surroundings. 
The height of the edifice that is to be delineated in perspective will in 
each instance establish the distance that the station point should be from 
the picture plane by geometrical principles, inasmuch as the location of 
the station point moves in a circumferential line from the center of the 
semi-circle, the degree of the angle from which the object is viewed will 
increase or be decreased accordingly. 

The eye will see indistinctly all objects that come within the range of 
vision, inasmuch as only one point on the object can be seen distinctly 
at the time the attention is concentrated upon it, all the other points on 
that object will be indistinct in proportion to the distance that they are 
from this central point; when this distance is increased until a line con- 
necting the two points subtends an angle of thirty degrees then the re- 
ceding point becomes invisible, therefore an angle of thirty degrees may 
be considered as the limit for the plane of clear vision. A figure consisting 
of two semi-circles representing that which is seen from the station point, 
the central point being the plainest in its apparent detail. This figure 
is then evolved into a figure consisting of three semi-circles, the two 
smaller within the larger, then the points remote from the center of 
vision will be seen at an angle of one-hundred and eighty degrees on a 
horizontal plane, it is likely that some individuals are able to see at this 
angle vertically, though all the points on the object will be indistinct in 
proportion to their distance from the central point. 

The distance the vanishing points are from the station point, will 
be as the distance the station point is from the picture plane, multiplied 
by the cotangent of the angle of view. The measuring points for any angle 
of view, is the same distance on the horizon from the vanishing point, as 
the station point is from the vanishing point. 

15 



Perspective Delineation 

To locate M use V as a center and V'S as a radius, inscribe an arc 
of a circle S M. To locate M' use V as a center and V S as a radius, 
inscribe an arc of a circle S M\ The vertical line S P C, from the station 
point to the picture plane, is the axis line or the line on which all the 
heights are to be laid off to scale measurements for the perspective. The 
position C on the picture plane is the point around which the whole group 
of objects are rotated. The various points at which this position can be 
located in perspective delineation is shown on the block perspectives. 
Plates No. 38 to W inclusive. 

Parallel Perspective 

The purpose of illustrating a technical work on perspective, is to 
convey to the mind of the reader, by illustration and description, 
the method of delineation used in the preparation of the plates, so 
that it can be followed up through the various manipulations, from a 
perspective nucleus to a completed perspective. These plates have been 
referred to when discussing the various technical terms as used in perspec- 
tive, and are so arranged that each problem is a stepping stone to the 
desired goal; starting with the elementary problems and continuing to 
problems of more complex nature, that will require greater initiative on 
the part of the delineator in their execution. It is not intended that these 
plates should be copied line for line, but are to be referred to when desiring 
to obtain a solution for similar problems in perspective. 

The rudimentary conception of perspective delineation was a perspec- 
tive drawn with one vanishing point and a measuring point on the horizon, 
in which the picture plane is assumed to be parallel with one of its faces, 
the parallel lines nearest the observer are drawn so that the vertical and 
horizontal lines intersect at right angles, the parallel lines on the opposite 
side converge to a vanishing point on the horizon. This method of per- 
spective drawing, though the simplest, should not be used for drawing 
perspectives of any pretense, as the defects are so apparent, that the per- 
spective would appear as though it was distorted. It is better adapted 
to drawing small perspectives and geometrical demonstrations, such as 
entrance motives, cornices and other details, when it is desired to study 
them in perspective. 

We shall now consider the position of the station point, or where the 
observer is located when viewing an object, that is to be drawn in parallel 
perspective, on Plate No. 24, there are three rectangles of the same 
dimensions, drawn from three angles of view, fifteen, thirty, and forty-five 
degrees to the picture plane, with a line drawn from the point of inter- 
section with the picture plane, to a point, to intersect with the circum- 
ference of the semi-circle, which locates the station point of the observer 
starting with forty-five degrees, where the distance from the station point 
to the picture plane is the greatest, and continuing in a circumferential 

16 



Perspective Delineation 

line to the station point, where the angle of view is fifteen degrees; the 
rectangle is set to form an acute angle on the left hand side of fifteen 
degrees, on the right hand side an acute angle of seventy-five degrees, to 
the picture plane, the observer is then very close to the object; as a semi- 
circle three feet in diameter, and a perspective drawn an eighth of an 
inch to a foot, for this angle of view, the station point would be thirty-six 
feet from the picture plane, or the corner of the object, if the observer 
approached the object so that the angle of view was one degree, he would 
then be standing as close to the object as would be consistent, unless he 
desired to ascend its perpendicular walls ; therefore he could only see the 
part that was immediately in front of him. However, this need not be 
the situation, the angle of view of the object, can be ninety degrees and we 
shall still be able to draw it in perspective, we can move away from it, so 
that the viewpoint is parallel with one side of the object, and the picture 
plane is parallel with the front of it, the horizontal lines on one side will 
converge to the vanishing point on the horizon, on the front they will 
intersect with the vertical lines at right angles, then the perspective will 
be drawn in parallel perspective. 

The station point, and the vanishing points will be equal distances 
from the center line of the semi-circle, as it is in a perspective drawn at 
an angle of forty-five degrees, or the center of the semi-circle is the 
vanishing point V, and the vanishing point V, is the station point, so in 
order to see the object, the vanishing point will have to be moved along to 
a point on the picture plane, equal to about one-half, or one-third, of the 
distance from the center of the semi-circle, to the station point, the station 
point is moved an equal distance, to that of the vanishing points; but 
the position of the object remains where it was at the start, the measuring 
point, is the same distance from the vanishing point, as the station point, 
then the angle of view of the object is at ninety degrees. 

Plate No. 1. All objects are drawn in perspective, as they would ap- 
pear to the eye, projected on the picture plane from a station point. The 
upper figure shows how an object when projected on the picture plane, 
will appear in perspective, the picture plane is inserted between the object 
and the station point of the observer, and is parallel to one of its faces; 
in this instance there will be a foreshortening in the height as well as 
in the width of the object. 

The lower figure is projected on two planes, viewed from different 
station points. The object can be viewed from any angle of view, and 
would be approximately the same in profile, the height of the object as 
projected would be elongated, or foreshortened, according to the distance 
the picture plane is from it, as the picture plane is set closer to the object, 
the projected image will be greater in height, as the picture plane is moved 
toward the station point of the observer, there will be a foreshortening 
in the apparent height of the projected image. 

17 



Perspective Delineation 

Plate No. 2. The picture plane is inserted between the observer and 
the object, illustrates how the height of the objects in geometrical eleva- 
tion, are foreshortened by perspective, as they recede from the eye, by the 
parallel lines piercing the picture plane ; the upper illustration shows how 
they appear in perspective. The measuring point and the vanishing point 
should be located on the horizon with the ground line drawn about four 
and a half feet below the horizon, or the height of the observer's eye, the 
height of the lamp posts should be laid off on the line a b and a line drawn 
from a to V and one from b to V ; this will give the height of the lamp posts 
in perspective, as they recede from the eye, they are spaced equal distances 
apart on the ground line, at the points c, d, e, f and g, a line drawn from 
c to M, at the point of intersection with b V will be the center of the first 
lamp post on the line b V, a line from d to M at the point of intersection 
with b V, will be the center of the second lamp post, the same operation 
should be repeated for the lamp posts located at the points e, f , and g, after 
these points on the line b V are located, draw perpendicular lines through 
them to the line a V, which will be the center lines of the lamp posts, and 
show how they appear on the picture plane to the observer in perspective. 

Plate No. 3. When arches and ellipses are to be drawn in perspective, 
they should be drawn from projected points on the orthographic plan, to 
points of intersection in perspective ; for small arch openings, by dividing 
the semi-circle into quarter parts, the points of intersection of the vertical, 
horizontal and quarter axis, on the semi-circle are sufficient; but for 
larger arch openings, these should be subdivided for the sake of accuracy. 

A semi-circle in perspective appears like an ellipse in a geometrical 
elevation, an ellipse in perspective like a semi-circle in a geometrical eleva- 
tion. The arch openings on Plate No. 8 for semi-circular arches, illustrates 
how these points are projected from the orthographic plan to the perspec- 
tive ; draw a semi-circle in plan and divide it into four equal parts, this gives 
the vertical, horizontal and quarter axis, project these points to the ground 
line by the measuring point, then vertically to the perspective. Draw a 
semi-circle with a radius of one-half of the diameter of the arch opening 
in the geometrical elevation, and project from the horizontal, vertical, and 
the quarter axis points to the perspective, by using the point V, at the 
intersection of these axis points in perspective, draw the arch ring in 
perspective. 

A series of arches in any plane, can be drawn in perspective by pro- 
jecting in the manner above described, by laying out the width of the 
openings on the ground line, projecting to the ground line in perspective 
by the measuring point M; from these points of intersection draw per- 
pendicular lines to intersect with the lines projected horizontally from the 
axes points, to the vanishing points, then draw the arch rings in 
perspective. 

18 



Perspective Delineation 

Plate No. U- The picture plane is inserted between the station point 
of the observer and the geometrical elevation of the object, illustrating 
the method of projecting from designated points on the object, to the 
picture plane, giving the foreshortening in perspective. These points are 
projected to the station point of the observer by continuing them on a 
horizontal plane to a line at forty-five degrees, then projecting vertically to 
a line drawn at the same angle ; starting from the ground line and pro- 
jecting horizontally to a perpendicular line in the plane of the station point 
of the observer. 

A line drawn from the station point of the observer to V, on the 
horizon will give the ground line in perspective, the same points that were 
projected horizontally to the station point of the observer, are to be pro- 
jected vertically from the object to the ground line. The measuring point 
M, should be located on the horizon. A line drawn from e to M at the 
point of intersection with e V, at e gives the starting point for drawing 
the perspective, draw a vertical line from e to where it will intersect with 
the line drawn from d, in the plane of the station point to V, this will be 
the height of the object in perspective, draw a line from k to M, at the point 
of intersection with e V, draw a vertical line to intersect with d V, this 
will be one side of the object in perspective. 

Plate No. 5. The drawing of a perspective is analogous to drawing 
the geometrical elevations from the orthographic floor plans. The ortho- 
graphic plan of the edifice, should be drawn as though it was laid out on 
the surface of the earth and a perspective drawn of it; this can be ac- 
complished by drawing a horizontal line across the drawing paper, bisect- 
ing it for the center line ; at each extremity of this line, place a vanishing 
point V and V, bisect the distance from the center line to the point V, 
and drop a perpendicular line to an indefinite point, with a set square 
of thirty and sixty degrees draw a line from V to intersect with this per- 
pendicular line, this point of intersection we will call S P, and the inter- 
section with the horizontal line or the picture plane, this point will be 
called C, draw a line from S P to intersect with the vanishing point V, 
the figure just completed is a large right angled triangle, and is divided by 
the line C, S P, forming two smaller right angled triangles within the larger 
one. Using V S as a radius, draw an arc of a circle equal to V M', with V S 
as a radius, draw an arc of a circle equal to V M — M and M' are the 
measuring points for the perspective in plan. Draw a line arbitrarily 
placed, parallel to the line on which the vanishing and measuring points 
are located, and equal in length to it, this is the line of measures or 
measuring line, lay off on this line, from the point of intersection with the 
line C to S P, on the left hand side, a distance equal to the dimension of 
one side of the object, that is to be drawn in perspective, as indicated by 
the letters a b on the plate, on the right hand side of this line, lay off the 
distance equal to the other side of the object b c, draw a line from b to V, 

19 



Perspective Delineation 

and one from b to V, this gives the two sides of the building in perspective 
plan without any definite length, draw a line from c to M, at the point of 
intersection f, on the line from b to V, draw a line to V, from a, draw 
a line to M', at the point of intersection d, on the line b V, draw a line 
to V intersecting the line f V at e; the figure just completed is the per- 
spective in plan of the building, as it would appear if it was laid out on 
the surface of the earth. The openings in the wall and the roof lines in 
the perspective in plan, are obtained by the same method of projection, 
by first laying them out on the measuring line, projecting them to the 
perspective in plan, then projecting these points from the perspective in 
plan perpendicularly to the perspective, and the heights from the 
geometrical elevation to intersect with those from the plan, by this method 
a perspective can be drawn, as it will appear on the picture plane from 
the station point. 

Plate No. 6. When an interior is drawn in parallel perspective, the 
picture plane is assumed to be parallel with one end of the room, the sta- 
tion point will be a short distance back of this plane, where the picture 
plane is set perpendicular to the horizontal plane of the floor. The vanish- 
ing point is on level with the eye of the observer, and is usually in the center 
of the end of the room, that is parallel to the picture plane, although it 
can be set a little to one side if desired. The measuring point should be 
located on the horizon, equal to the distance the station point is from 
the vanishing point, either to the left or to the right of the point V. 
The station point for drawing a parallel perspective of an interior, should 
not be taken at too great a distance from the picture plane, as the fore- 
shortening in the side walls will be greatly increased and appear obliquely 
or edgewise, while a fuller view of the walls will be had, if the station point 
is nearer the picture plane, the position of the station point should be 
placed, by assuming a reasonable distance for the depth of the room. 

Drawing a perspective in plan, for an interior, that is to be drawn 
in parallel perspective, enables the delineator to be more accurate in the 
projection of the points perpendicularly, to the perspective, the preliminary 
part of the work can be done on a separate sheet of paper, then pinned 
down over the paper on which the perspective is to be drawn. The line 
a d in the perspective is used as a ground line for the perspective in plan. 

Lay off on the ground line a d, the openings in the side wall, these are 
to be projected to a line drawn from a to V, from the points g, h and i, 
draw lines to M ; at the point of intersection with the line a V, gives the 
openings in the left hand side wall and the corner of the room, these points 
are to be projected perpendicularly to the perspective, from the points of 
intersection with the line a B in perspective plan, draw perpendicular lines 
for the height of the openings, as laid off on the line a b. If the openings 
are duplicated in the right hand wall, the points of intersection on the line 
a V, can be drawn horizontally across in the perspective in plan, to the 

20 



Perspective Delineation 

line d V, it will then be a repetition of the method as described. However, 
should they not be duplicated in the right hand wall, then the openings 
in that wall should be laid off on the line a d, and projected to d V, then 
projected horizontally across in the perspective in plan, to the line d V, and 
projected perpendicularly to the perspective, or another measuring point, 
M' should be established on the right hand side of V, equal to the distance 
that M is to the left of V, and the openings laid off on the line a d, start- 
ing from the point d and drawn from these points to d V in perspective 
plan, then projected perpendicularly to the perspective. The openings in 
the end wall of the room, are to be laid off on the ground line a d, and lines 
drawn from these points to V, to the point of intersection with the line 
from e f, then projected perpendicularly to e f in the perspective, the 
height of these openings should be projected from the line a b to V at 
the point of intersection with the line e and e they are to be drawn horizon- 
tally across the end wall. 

Plate No. 7. An interior of a room drawn in parallel perspective and 
compared with a photograph taken from the same viewpoint, the photo- 
graph would show a slight convergence to the horizontal lines that enclose 
the end wall of the room, compare Plates No. 6 and 7. The apparent 
reason for this is that the lens in the Kodak conveys an image of the 
objects to fhe photographic plate in the same manner as the crystalline 
lens in the eye receives the rays of light reflected from objects. The lens 
in the Kodak is ground so that the rays of reflected light fall upon the 
photographic plate, in the same manner as they do upon the retina of the 
eye ; although this slight convergence may not be apparent to the observer, 
yet it is present, and if we are to draw it in perspective as we see it, these 
lines would not be horizontal, as they converge to a vanishing point, ac- 
cording to the viewpoint of the observer, see Plate No. 32. Interiors are 
not satisfactorily drawn in parallel perspective, as the openings in the side 
wall pass beyond the plane of vision very quickly and appear distorted ; a 
better view of the room is obtained by drawing it in angular perspective, 
showing only two sides of the room as illustrated on the plate referred to. 

Plates Nos. 3 and 9. Street scenes can be drawn in parallel or angular 
perspective, at the delineators discretion ; parallel perspective though more 
often used for perspectives of this character, will at some time bring up 
a question that can not be readily solved. To what vanishing point do 
the lines a b converge, that run at right angles to those that converge to 
the vanishing point? For this question there is no answer in parallel 
perspective as they will have to be drawn horizontally, at right angles 
to the vertical lines that enter into the composition of the motives. 

A solution for this problem is illustrated on Plate No. 9. The same 
scene is drawn in angular perspective, in which the horizontal lines con- 
verge to a vanishing point V, and continue to rise as they pass beyond 
the plane of vanishing point V, from this point they pass beyond the plane 

21 



Perspective Delineation 

of vision of the observer from the station point. This convergence will be 
apparent in photographs taken from the same station point, the horizontal 
lines continue to rise as they pass beyond the plane of the vanishing point, 
and will appear slightly distorted. 

Oblique Perspective 

OBJECTS drawn in oblique perspective will have a convergence point 
for the vertical and horizontal lines entering into the composition of 
the motive. This convergence point will be in the plane of the vanish- 
ing point. A cube drawn in oblique perspective will have three vanishing 
points two for the horizontal and one for the vertical lines forming the 
three faces of the cube. Objects with inclined sides such as cones and 
pyramids, the convergence point for their inclined sides will be in the 
apex, over the center of the base, with two vanishing points for the lines 
composing their bases, Plate No. 10. Boxes loaded on one side or where the 
load is at rest in one corner of the box and they are floating in water, there 
will be three vanishing points for their delineation in perspective. Two 
vanishing points for the parallel lines forming the top and bottom of the 
boxes and one for the vertical lines enclosing the ends of the boxes in 
oblique perspective. The inclined post will have three vanishing points, 
one for the boundary lines of the post, and one for the sign board, the third 
vanishing point for the reflection on the water, these vanishing points will 
be in the plane of the vanishing point on the horizon. Plate No. 11. 

Plate No. 12. Parallel lines that are oblique to the picture plane, 
have their vanishing points in space, in the plane of the vanishing point 
on the horizon. Parallel lines composing hip roofs, valleys, gables, 
pediments and diagonals, when drawn in perspective, these lines vanish 
to points above and below the level of the eye. The height of the gable c d, 
is measured on the vertical line from b to b', a line drawn from b' to 
V, will intersect with the vertical line c d, in the center line of the rect- 
angle, this will be the apex of the gable roof, a diagonal line drawn from 
b to d, and extended to the plane of the vanishing point V above the horizon, 
will locate the vanishing point V ', which will be the vanishing point, for 
all parallel lines in the plane of the gables for the three edifices, on that 
side of the center line of the rectangle. A line drawn from d to intersect 
with the point e on the rectangle a b e f , and extended from d to the 
plane of the vanishing point V, below the horizon will locate the vanish- 
ing point V ' ', which will be the vanishing point for all parallel lines in 
the plane of the gables, on the other side of the center line of the rectangle. 
By this method of projection, the vanishing point for any system of lines, 
in any plane that is oblique to the picture plane can be obtained. 

The three edifices of the same type can be drawn in perspective by 
any desired method, the station point method of the perspective in plan 
method, or by constructing a series of rectangles, in which their apparent 

22 



Perspective Delineation 

width decreases according to their distance from the station point, after 
constructing the rectangle a b e and f, the height of the other two rec- 
tangles, will be as the height of the first, is reduced by the convergence of 
the parallel lines to the vanishing point V, after the first rectangle is con- 
structed and the vanishing points set off on the horizon, any number of 
similar rectangles can be constructed as each successive repetition, will 
be reduced in magnitude as it recedes from the eye. 

The Station Point Method of 
Perspective Delineation 

FOLLOWING up the rudimentary methods of perspective delineation, 
through the various stages that the principles of perspective were 
developed, it was readily found that all perspectives could not be 
drawn with one vanishing point ; or that a perspective from various points 
of view could not be drawn satisfactorily in parallel perspective, on 
account of the numerous limitations that surround this method. This 
method was evolved into a system, in which two vanishing points and an 
orthographic plan were used, using the station point as a measuring point 
for obtaining the foreshortening in perspective. When the orthographic 
plan is set in position, for the different angles of view on the picture plane, 
from its first position in parallel perspective the position of C is being 
moved in a horizontal line the orthographic plan forming acute angles 
with the picture plane; the station point also is moving in a circum- 
ferential line from the center of the semi-circle, following that of the 
orthographic plan, starting on the left hand side and finishing on the right 
hand side of the center line of the semi-circle. Plate No. 2k- When the 
station point is moved in a radial line from the center line of the semi- 
circle, for any angle of view, and lines drawn parallel to the boundary 
lines of the orthographic plan, to a point where they will intersect with 
the picture plane, they locate the vanishing points for the perspective, 
which will then be drawn by the station point method. The station point 
method of perspective delineation, has always been used by delineators for 
drawing perspectives of any pretense ; it can be said, that it combines all 
the elementary principles, that are used in the delineation of perspectives, 
into a composite form, to make a complete method of perspective drawing. 
To start a perspective by the station point method, the orthographic 
plan should be placed at the head of the drawing board, set to form acute 
angles with the picture plane. We will consider that the edifice is 
rectangular in plan, and the angles formed with the picture plane is 
thirty degrees on the right hand side, and sixty degrees on the left hand 
side of the point of intersection ; the preliminary part of the work is now 
complete, the next step will be to draw a line downward, the length of 
this line to scale will be one hundred and sixty-six feet from the picture 

23 



Perspective Delineation 

plane. The vanishing points are located by drawing line parallel to the 
boundary lines, or sides of the orthographic plan, starting from the sta- 
tion point and continuing until they intersect with the picture plane, 
forming acute angles, respectively, of thirty and sixty degrees. 

In this instance the right hand vanishing point will be out in space. 
This difficulty could be overcome by placing two drawing boards together, 
but space will not usually permit. The exact location of this vanishing 
point can be obtained by calculation and an arc of a circle drawn to this 
radius, but as a rule delineators are not mathematicians, and are likely to 
overlook this important part of their work, so vital to perspective, guessing 
at an arc of a circle, considering that it will answer the purpose; con- 
sequently the results will be badly distorted perspective or a perspective 
with a very slight convergence to the parallel lines on one side of the 
edifice and converge too rapidly on the other. 

A method resorted to by delineators when using the station point 
method, and one or both vanishing points are out in space, is to divide 
the vertical line from the station point to the picture plane, into three or 
four equal parts, drawing small right-angled triangles within the large 
right-angled triangle; Plate No. Ik, by this method the altitude will be 
reduced to one-quarter of its actual height, then its length can be con- 
veniently scaled. In this problem it is one-quarter of one-hundred and 
sixty-six feet, or forty-one feet and six inches ; draw a line from this point 
on the base, to an angle of sixty degrees, to where it will intersect with 
the altitude line, then scale the altitude of the small right-angled triangle. 
By calculation and the method above described, results are approxi- 
mately the same. The altitude of the large right-angled triangle will 
be four times the altitude of the smaller one. We have now obtained 
the distance it will be to the vanishing point, that is out in space. Sub- 
tracting the distance it is from the vanishing point, to a point that will 
be on the drawing board, and the concave side of an arc of a circle, from 
the altitude of the large right-angled triangle, the result will be the radius 
of an arc of a circle. By cutting a curve out of a piece of cardboard or 
similar material to this radius, and securing it to the drawing board, it 
will serve the purpose of a convergence point, for all horizontal lines in 
that plane. 

The method of using cardboard or wood curves for the delineation of 
perspective, when both vanishing points are out in space, for very large 
perspectives is illustrated on Plate No. 15. The various positions in which 
the tee-square is drawn, shows how the parallel lines on both sides of the 
object, can be drawn to a vanishing point that is out in space ; by placing 
the cardboard curves back to back, attached to the left hand side of the 
drawing board. 

The tee-square when using the cardboard curves, should have the 
upper edge of the tee-square blade, in the center of the tee-square head. 

24 



Perspective Delineation 

If this pattern of tee-square is not to be had, the ordinary tee-square can 
be utilized for the purpose by driving two brads in the upper side of the 
tee-square head, at points that will bring the upper edge of the tee-square, 
in the center of the tee-square head. 

The delineation of perspectives with the cardboard curves as described, 
have many disadvantages, that need not be described here, as all delineators 
are familiar with them, and should only be resorted to when another 
method can not be used. A set of curves should be cut for each perspective, 
or perhaps more, as the point of view first selected may not be desirable, 
if this should happen to be the situation, the first set of curves cut should 
not be used for the same perspective if the angle of view is changed and 
the perspective is to be drawn mathematically correct. 

The foreshortening in perspective is obtained by placing the straight 
edge or tee-square, using the station point as a measuring point, and draw- 
ing parallel lines from the points on the orthographic plan, to the picture 
plane. Dots or dashes may be used at the delineators discretion, all 
openings in the wall and projections beyond the wall, should be indicated, 
along with the other subordinate objects, that will appear in the perspec- 
tive. After this part of the preliminary work has been completed, the 
vanishing points can be brought down to a line, drawn across the paper 
representing the horizon, and drawing of the perspective started. Plate 
No. 13. 

Delineators while performing the various manipulations with the 
tee-square, in the drawing of perspectives, have no doubt experienced that 
the tee-square head is often a disadvantage, when attempting to do rapid 
work, as all the converging horizontal lines are drawn with the tee- 
square, the vertical lines with a set square or triangle. In order to draw 
the converging horizontal lines on the right hand side, of the point C, 
the tee-square has to be turned over, or the blade will be the thickness of 
the tee-square head above the drawing board, in order to reach the vanish- 
ing point, on account of the shortness of the blade; a tee-square with a 
long blade has also its disadvantages. 

These difficulties will be overcome by using a straight edge, or a tee- 
square with the head removed, movable pins or brads should be driven into 
the drawing board, at convenient points, as illustrated on Plate No. 16, 
which will facilitate matters to a great extent, and lessen the mental 
anxiety on the part of the delineator. Straight edges of different lengths 
will be found convenient for rapid work. 

Continuing the usual practice in the delineation of perspectives, by 
the station point method, setting the orthographic plan in position, with- 
out considering what parts of it will project beyond the picture plane. 
The point of intersection of the orthographic plan, is usually one corner 
of the edifice, although this is a matter for the delineator to decide, as 
there will be no unusual conditions arise, if the point of intersection with 

25 



Perspective Delineation 

the picture plane, was taken at some point on the projecting cornice, or 
the picture plane cut through the wall back of the corner if desired; 
however, there is no apparent reason for it, as there is a tendency toward 
making unnecessary work; for there will be in most instances, some part 
of the plan that will project beyond this plane, when it is set in position. 

The foreshortening in perspective is obtained in the usual manner, 
by drawing parallel lines from the points on the plan to the picture plane, 
for those parts of the edifice that lie back of this plane. The picture plane 
in this instance, cuts through a portion of the projecting wing of the 
edifice, this will present a different condition than that which we have 
been accustomed to. Instead of following the usual method of projecting 
the points on the plan, to the picture plane, for the portion of the edifice 
that lies back of it, in this instance it will be the reverse of the method 
described ; the points on the plan will be projected back to the picture plane, 
by using the station point as a measuring point. The point a is projected 
to a' on the picture plane, which gives the corner of this wing in perspec- 
tive. This same method of procedure should be followed for all the other 
motives, in the portion that projects beyond this plane, by this method of 
projection all points in the portion of the edifice that project beyond 
the picture plane are obtained for the perspective. Plate No. 17. 

The essential features of this method are correspondingly the same 
as used before, but the method of procedure is slightly different. 

It is to enlarge upon the methods now in practice, and permit the 
delineator a wider range of operations with less limitations. Heretofore 
in order to start the preliminary work on a perspective, the orthographic 
plan was set in position at the head of the drawing board, some part of 
which was brought to a point of intersection with the picture plane, or 
set a short distance back of it, forming acute angles with this plane; the 
station point was then located and the position of the vanishing points 
obtained after obtaining the foreshortening in perspective in the usual 
manner the delineator was ready to start work on the perspective. The 
same method of procedure has been used in this problem with some 
modifications. 

To start the preliminary work for a perspective by this method, it 
will be necessary to first assume the diameter of a semi-circle, this will be 
governed by the length of the drawing board, and the size of the perspec- 
tive to be delineated; a semi-circle three feet in diameter for small per- 
spectives and four feet in diameter for all average perspectives, a semi- 
circle five to seven feet in diameter is ample for all large perspectives. A 
line drawn across the paper representing the picture plane, should be 
bisected for the center line of the semi-circle, from this point the position 
of C can be established by calculation, or that part of the orthographic 
plan that will intersect with the picture plane. The position C, is the 
point about which the orthographic plane of all of the edifices, that are to 

26 



Perspective Delineation 

be drawn in perspective is rotated, and is in a direct line with the station 
point, where the observer stands while viewing the objects. The delineator, 
in his endeavors to obtain a desirable view of the objects by changing the 
angle of vision is moving the position of the station point, in a circum- 
ferential line from the center of the semi-circle. By moving the station 
point about in this manner, the view of the entire group is changed and 
the distance between the center line of the semi-circle and the position of 
C, will be increased or decreased accordingly; but the position of the 
vanishing points remain as they were established by the assumed 
diameter of the semi-circle. The position C when the angle of view has 
been chosen should be checked by calculation, as it has a fixed relation 
to the diameter of the semi-circle. Plates Nos. 13 and 2U. In the column of 
figures headed degree of angle on left, gives the angles of view from ten 
degrees to eighty degrees, the angle of view at which the orthographic 
plan is to be set, should be chosen; that which gives the most desirable 
point of view of the edifice, for this problem we will use an angle of thirty 
degrees, the next column of figures headed degree of angle on right is an 
angle of sixty degrees so the perspective will then be drawn to angles 
of thirty and sixty degrees. Assuming the drawing board to be four 
feet long and this dimension is to be used for all calculation, (for con- 
venience of calculation fractions of a foot should be avoided.) In the next 
column of figures headed C, and for the same angle of view — multiplying 
this figure by the diameter of the semi-circle ( — .2500 x 4) and the result is 
— 1.0000 equivalent to 1' — 0", the sign before it is minus, so it will be laid 
off on the picture plane, on the left hand side of the center line of the semi- 
circle. This is one corner of the building, or the point at which the 
orthographic plan intersects with the picture plane. The ortho- 
graphic plan can now be set in position, forming acute angles with 
the picture plane, of thirty and sixty degrees. In the column of figures 
headed S P, or station point, for the same angle of view — multiplying this 
figure by the diameter of the semi-circle and the equivalent of the scale 
used for the perspective to actual size (.4323 x 4 x 96) the result is 166.00 
or 166' — 0", this is the distance the station point is from the picture plane, 
and is to be laid off on a vertical line intersecting the picture plane at the 
point C. The results obtained by these calculations will be in feet and 
decimals of a foot, and are to be converted into feet and inches, from tables 
in text books giving these equivalents, they can be laid off on the picture 
plane with a scale or a ruler. By this method the position of C, or the 
point of intersection of the orthographic plan with the picture plane, and 
the distance to the station point on the circumference of the semi-circle 
have been found by a method of calculation, the right and the left hand 
vanishing points have been established by the diameter of the semi-circle. 
The plus and minus signs before the figures in the column headed C, 
indicate that these positions are to be laid off to the left, or to the right, 

27 



Perspective Delineation 

of the center line of the semi-circle, minus is to the left and plus is to 
the right. 



Degrees of angle on left 


Degrees of angle on right 




c. 


S.P. 


10 




80 






—.4688 


.1719 


15 




75 






—.4323 


.2500 


20 




70 






—.3802 


.3229 


25 




65 






—.3229 


.3854 


30 




60 






—.2500 


.4323 


35 




55 






—.1719 


.4688 


40 




50 






—.0885 


.4896 


45 




45 






+.0000 


.5000 


50 




40 






+.0885 


.4896 


55 




35 






+.1719 


.4688 


60 




30 






+.2500 


.4323 


65 




25 






+.3229 


.3854 


70 




20 






+.3802 


.3229 


75 




15 






+.4323 


.2500 


80 




10 






+.4688 


.1719 


Scale equivalents to actual 


3ize. 










1/2" to 


one foot = 


1/24 actual size 






3/8" " 




' = 


1/32 ' 


t n 






1/4" " 




' = 


1/48 * 


< << 






3/16" " 




' = 


1/64 ' 


t ti 






1/8" " 




' = 


1/96 


l a 






3/32" " 




' = 


1/128 ' 


I a 






1/16" " 




' = 


1/192 ' 


< a 





After the preliminary part of the work has been completed, and the 
foreshortening in perspective obtained in the manner heretofore described, 
then the vanishing points should be brought down to a line drawn across 
the paper, representing the horizon and the work on the perspective 
started. 

Delineators will readily see the great amount of work that has been 
eliminated by this method, as it establishes the position of the various 
points used in perspective delineation, by a method of calculation, that is 
very simple, and if it is desired to change the angle of view, it will be 
repetition of the method as described. The position of both vanishing 
points have been definitely located, if one of them is off the drawing board, 
it is a simple matter to locate a point that will be on the drawing board, 
that distance minus one-half the diameter of the semi-circle will be the 
radius of an arc of a circle, for the convergence of the parallel lines in 
that plane. 

Perspective Plan by the Station Point Method 

BY forming a mental concept of the orthographic plan of the edifice, 
as it would be laid out on the surface of the earth from which the 
building is to be erected, we have then a mental picture in mind 
of the perspective in the plan of that object as we proceed to erect mentally 
the enclosing walls and construct a roof on these walls it will complete our 



28 



Perspective Delineation 

mental concept of the edifice in a perspective in plan. Throughout this 
mental operation, we have at all times viewed the object as it would be 
erected on an orthographic ground plan in perspective from a station 
point and maintained the same angle of view. Retaining this mental 
concept in the manner it was first conceived we shall now undertake to 
draw the perspective in plan, not on the surface of the earth, for we are 
not accustomed to drawing on substances of earthy consistency, and to 
actual size, but we shall draw it on paper, to a small scale from which 
we will draw a perspective. 

The average delineator when using the station point method, has 
made no use of the perspective in plan, that can be drawn by this method, 
as shown in the illustration on Plate No. 13. If the perspective in plan 
method is adopted by the delineator, it would eliminate considerable un- 
necessary repetition, and enable the delineator to follow up each suc- 
cessive step as the work progressed, without referring again to the ortho- 
graphic plans and the station- point ; these plans should show all the details 
that are to be drawn in perspective by perspective projection. 

A perspective of a building, in which the design varied somewhat in 
the successive stories, a perspective plan should be drawn of each story, 
where there was any modification of the motives making up the com- 
position. A perspective plan of the two sides of the building is all that 
need be drawn, in a six-story building, a plan of the first and second floors ; 
the next three stories or perhaps more as the case may be, these would be 
alike in many details, only one plan need be drawn; a plan of the upper 
story, as there is likely to be some modification in the motives making up 
the composition, the plan of this story should show belt courses and other 
details, brackets, projections, brakes in the cornice and the planes of 
the various projections beyond the face of the wall, and the parapet 
walls ; this should also show the small buildings on the roof, such as pent 
houses, skylights and smoke stacks, if they are to appear in the perspective. 
These plans should be complete, so the delineation of the perspective can 
be carried on without interruption. 

The development of the perspective in plan, in connection with the 
station point method of drawing a perspective, is the only method in the 
mind of the author, in which inaccuracies and distortion, in architectural 
perspective can ultimately be avoided. The station point method of 
perspective delineation without developing a perspective in plan, involves 
considerable guess work on the part of the delineator ; on account of the 
confusing array of points on the picture plane, as they are always a pos- 
sible source of error; the delineation will be often criticized and the de- 
lineator will have to allow himself to be at fault, as we all do not see things 
the same way. 

There are some examples of the perspective in plan, drawn by the 
station point method, although it seems not to be used extensively by 

29 



Perspective Delineation 

delineators. A perspective in plan drawn by the station point method, 
and a perspective in plan drawn by the perspective in plan method, if 
the distance to the station point is the same for both, they should con- 
form in all their respective dimensions. 

Perspectives By the Perspective 
In Plan Method 

tarting with the elementary principles of perspective delineation, 
and illustrating briefly the various stages of development, through 
which these principles have passed, before they were combined into 
one composite method of delineating perspectives by the Station Point 
Method; considering that we have not as yet reached the climax, in 
the development of these principles, and that there will be discoveries 
made, at some future time that have not as yet been conceived. 

The Perspective in Plan Method, is a further development or the 
evolution of the Station Point Method, as it continues to develop the 
elementary principles of perspective, that were combined into one method, 
for the delineation of Perspectives by the Station Point Method. Permit 
me to reiterate, that this statement is arbitrarily made with this sup- 
position in mind — that, when perspectives are drawn by the Station 
Point Method a perspective in plan is drawn in connection with it, to 
enable the delineator to be more accurate in his operations. 

Therefore, if we should draw a semi-circle one foot in diameter, and 
draw a perpendicular line through the center of the semi-circle, we have 
then located a point, from which all the required points for the delineation 
of perspectives by this method are obtained. The first point to be located 
is the point C, or the point of intersection of the orthographic plan with 
the picture plane, to locate this point we shall have to choose an angle 
of view; for this problem we will use an angle of thirty degrees on the 
left hand side, and sixty degrees on the right hand side, of the center 
line of the semi-circle. Take a thirty and sixty degree set square, lay 
it on the drawing, so that the longer side is parallel with the picture plane, 
and the apex coincides with the point of intersection of the picture plane 
with the semi-circle on the right hand side, the other point of intersection 
with the semi-circle, will locate the station point. A perpendicular line 
drawn from this point to the picture plane will locate the point C, on this 
plane, also draw a line parallel to the hypotenuse, or the longest side of the 
set square, to intersect with the semi-circle and the picture plane ; revers- 
ing the set square, so that its long side is parallel to the perpendicular 
line, from the station point to the position of C on the picture plane, and 
the apex coincides with the station point, draw a line to intersect, with 
the intersection of the picture plane with the semi-circle. By this method 
we have obtained the position of the left and the right hand vanishing 

30 



Perspective Delineation 

points V and V, the position of C on the picture plane, the point S, or 
station point on the circumference of the semi-circle ; the points obtained 
in this manner should be lettered as indicated on Plate No. 18. To locate 
the measuring points for obtaining the foreshortening in the perspective 
in plan, use V as a center and V'S as the radius, draw an arc of a circle 
to intersect with the picture plane, this will locate the point M. With V 
as a center and V S as a radius, draw an arc of a circle to intersect with 
the picture plane locating the point M', the second measuring point. The 
next measuring point to be located, will be for drawing all lines in the 
perspective in plan, that intersect the horizontal and vertical lines, at an 
angle of forty-five degrees. Take a forty-five degree set square, lay it on 
the drawing so that the hypotenuse, or its longest side, is parallel to the 
line drawn from S to V, the tip of one of its forty-five degree angles, co- 
incides with the point S at the point of intersection with the semi-circle 
locating the measuring point X on the picture plane, as illustrated on 
Plate 18. 

The perspective in plan method is a further development of the 
station point method, by using the measuring points to obtain the fore- 
shortening in perspective, in place of the station point as used in the 
station point method. The comparison between the two methods is 
obviously made, with this supposition in mind, that when the station point 
method is used by delineators, a perspective in plan is drawn, in which 
case there is one essential difference between the two methods ; it is neces- 
sary in the perspective in plan method to have a line of measures arbitra- 
rily placed between the picture plane and the station point, and is referred 
to as the measuring line, as in the station point method it is used as a 
secondary picture plane, when a perspective in plan is drawn in connection 
with this method of perspective drawing. 

The average illustration of the perspective in plan method shows a 
diagram with the two vanishing points and the measuring points located, 
with a perspective in plan drawn to an angle of thirty and sixty degrees, 
oh the left hand side of the center line of the semi-circle, or at forty-five 
degrees, limiting this method of perspective to these two angles of view. 
This leaves a wide margin of intangibility, and the delineator in desiring 
to use this method would have to draw a semi-circle the actual size, in 
order to locate the vanishing points, for drawing the perspective in plan. 
In this event it would be rather cumbersome method, as it would be neces- 
sary to inscribe a semi-circle three, four, or perhaps seven, feet in diameter, 
whenever a perspective is to be drawn, or draw a semi-circle of a smaller 
diameter and locate the measuring points, then transfer them by using the 
dividers to a semi-circle of larger diameter. A semi-circle seven feet in 
diameter may not seem large, but when working space is cramped it will 
be looked upon in a different manner. However, this method can be re- 
duced to a semi-circle of unit dimension, so that the whole operation can 

31 



Perspective Delineation 

be performed on the average sized drawing board, and the drawing of a 
large perspective becomes a simple matter. 

Perspectives are usually drawn to the same scale as the working 
drawings, although it is often advantageous to draw a perspective to a 
larger scale than the working drawings are made, on account of the fore- 
shortening in perspective. In this respect the perspective in plan method 
has the advantage over the station point method, as a perspective in plan 
is to be drawn, all the openings and projections are to be put into scale 
measurements, the use of a larger scale for the perspective in plan and the 
perspective will then be a matter of choice. 

When the perspective in plan method is used, a block perspective of 
the edifice can be made without detail and the perspective view considered, 
it may be desirable to use a different angle of view, on the left or on the 
right hand side of the center line of the semi-circle, all that will be required 
is a mathematical calculation and the shifting of the measuring points 
from one position to the other, and redrawing the perspective in plan. 

To start the preliminary work for a perspective by the perspective in 
plan method, we will first assume the diameter of a semi-circle, a semi- 
circle three feet in diameter for small perspectives and four feet in diam- 
eter for all average perspectives ; a semi-circle five to seven feet in diameter 
is ample for all large perspectives. We will assume that we are about to 
draw a perspective of the average size ; its plan, is a rectangle one hundred 
feet on the front and sixty feet on the side; the height is one-quarter of 
its length, or twenty-five feet. 

Assuming the diameter of the semi-circle to be four feet, and this 
dimension is to be used for all calculation (for convenience of calculation 
fractions of a foot should be avoided). In the column of figures headed 
"Degree of angle on left" are given the angles of view from ten degrees to 
eighty degrees. For this problem we will use an angle of thirty degrees, in 
the next column of figures headed "Degree of an angle on right," is an angle 
of sixty degrees, so the perspective will be drawn to angles of thirty and 
sixty degrees. In the next column of figures headed M, or the first measur- 
ing point and for the same angle of view, multiplying this figure by the 
diameter of the semi-circle ( — .3646 x 4) the result is — 1.4584, equivalent 
to 1' — 5V2'". the sign before it is minus, so it will be laid off on the picture 
plane, on the left hand side of the center line of the semi-circle. The next 
column of figures headed C, for the same angle of view, multiplying this 
figure by the diameter of the semi-circle ( — .2500 x 4) the result is 
— 1.0000, equivalent to 1' — 0", the sign before it is minus, so it will be laid 
off on the picture plane, on the left hand side of the center line of the 
semi-circle. In the next column of figures headed X, for the same angle 
of view, is the measuring point for all lines that are to be drawn in the 
perspective plan at an angle of forty-five degrees, such as mitre points, hip 
roofs and valleys ; this is to be multiplied by the diameter of the semi-circle 

32 



Perspective Delineation 

and laid off on the picture plane as indicated by the sign before it. In the 
next column of figures headed M', the second measuring point, this figure 
is to be multiplied by the diameter of the semi-circle (+.0000 x 4). The 
result of this calculation would be four ciphers; this position will be on 
the picture plane, on the center line of the semi-circle. In the last column 
of figures, for the same angle of view, under the heading S P or the station 
point, gives the distance the station point will be from the picture plane, 
this figure is to be multiplied by the diameter of the semi-circle, and the 
equivalent of the scale used to actual size (.4323 x 4 x 96) the result is 
166.00 or 166' — 0". As the station point is not used for obtaining the fore- 
shortening in perspective, in the perspective in plan method, this calcula- 
tion need not be made, unless it is desired to know how far the station 
point is from the picture plane, and the object that is to be drawn in per- 
spective. The results of these calculations are in feet and decimals of a 
foot, they are to be converted into feet and inches from tables in a text 
book, giving these equivalents, they can be laid off on the picture plane 
with a scale or a ruler. By this method the position of the measuring 
points, the point of intersection of the orthographic plan with the picture 
plane, or one corner of the building, and the mitre points or lines at an 
angle of forty -five degrees, have been found by a method of calculation; 
the left and the right hand vanishing points, were established by the 
diameter of the semi-circle, we are now ready to start work on the per- 
spective in plan. 



Degree of 


Degree of 












angle on 


angle on 












left 


right 


M 


C 


X 


M' 


SP 


10 


80 


—.4844 


—.4714 


—.3516 


—.3281 


.1719 


15 


75 


—.4661 


—.4349 


—.2917 


—.2448 


.2500 


20 


70 


—.4401 


—.3828 


—.2344 


—.1589 


.3229 


25 


65 


—.4063 


—.3229 


—.1823 


—.0781 


.3854 


30 


60 


—.3646 


—.2500 


—.1328 


+.0000 


.4323 


35 


55 


—.3177 


—.1693 


—.0859 


+.0755 


.4688 


40 


50 


—.2656 


—.0859 


—.0417 


+ .1432 


.4896 


45 


45 


—.2083 


+.0000 


+.0000 


+.2083 


.5000 


50 


40 


—.1432 


+.0859 


+.0417 


+.2656 


.4896 


55 


35 


—.0755 


+ .1693 


+.0859 


+.3177 


.4688 


60 


30 


+.0000 


+.2500 


+.1328 


+.3646 


.4323 


65 


25 


+.0781 


+.3229 


+.1823 


+.4063 


.3854 


70 


20 


+ .1589 


+.3828 


+.2344 


+.4401 


.3229 


75 


15 


+.2448 


+.4349 


+.2917 


+ .4661 


.2500 


80 


10 


+.3281 


+.4714 


+.3516 


+.4844 


.1719 


Scale equivalents to actual 


size: 










1/2" to one foot = 1/24 


actual size. 






3/8" ' 


t n 


1 = 1/32 


si < 








1/4" ' 


t (i 


' = 1/48 


" ' 








3/16" ' 


< c< 


' = 1/64 


(i t 








1/8" ' 


< II 


' = 1/96 


" * 








3/32" « 


< CI 


1 — 1/128 


a t 








1/16" « 


( << 


" = 1/192 


<< < 







33 



Perspective Delineation 

To start the perspective in plan, draw a horizontal line arbitrarily 
across the drawing, below the line representing the picture plane, on which 
the positions are located ; this will be the line of measures or measuring line, 
draw a vertical line to intersect with the position C, on the picture plane ; 
this will be one corner of the building that is to be drawn in perspective, 
the length and breadth of the building are to be laid off on the measuring 
line, A B and C, Plate No. 19. Pins or short brads should now be driven 
into the drawing board at the right and the left hand vanishing points, V 
and V and the position of the measuring points, M X and M'. The measur- 
ing points M and M' will only be used for obtaining the foreshortening in 
the perspective in plan, the measuring point X for lines at an angle of 
forty-five degrees, and where a shadow will be cast on a vertical wall 
surface, when the source of light is assumed to be at an angle of forty-five 
degrees; after the perspective in plan is completed, the measuring point 
positions can be removed. Draw a line from B to V and one from B to V, 
this gives the two sides of the building in perspective in plan, without any 
definite length. Lay off on the measuring line one hundred feet from 
B to C, draw a line from C to M, to intersect the line B V at f , from f draw 
a line to V ; this will be the front of the building in perspective plan. Lay 
off on the measuring line from A to B sixty feet, draw a line from A to M', 
at the point of intersection with the line BV at d, draw a line from d to V, 
intersecting the line fV at e. The figure just completed is the perspective 
in plan of the edifice, as it will be foreshortened by the angle of view from 
a station point. Bisect the line from A to B, draw a line from this point 
to M', to bisect the line Bd in the perspective in plan at g, from g draw a 
line to V, this line divides the perspective in plan into two equal parts, 
and forms the ridge of the hip roof, from B draw a line to X, to intersect 
the line gV at h, and a line from X to e continued to intersect the line from 
g to V, from d draw a line to the point h and one from i to f, these lines 
from the hip roof in perspective in plan. The pins in the measuring points 
can now be removed, as the perspective in plan will not be carried further 
for this problem, tracing paper should now be pinned down over the per- 
spective in plan and work on the perspective started. A line representing 
the horizon should be located, it is always on level with the eye of the 
observer, about four feet and six inches above the ground line, the ground 
line is where the vertical wall surfaces meet the surface of the earth. 
Draw a perpendicular line representing the corner of the building in 
perspective, at the intersection of this line with the horizon line, measure 
off four feet and six inches below this point, for the position of the ground 
line. The left and the right hand vanishing points, V and V, should now 
be brought down to the horizon line, in the same positions on the horizon 
line, as they were on the line of positions for the perspective in plan, that 
is the distance between them should be the diameter of the semi-circle. 

34 



Perspective Delineation 

A line drawn from the corner of the building, at the ground line to V and 
one to V, gives the ground line in perspective. 

The height of the building should now be measured above the ground 
line, on the corner of the building and a line drawn from this point to V 
and one to V, this gives the height of the building in perspective. From 
the perspective in plan, on the left hand side, also on the right hand side, 
giving the length of the building, as foreshortened by the perspective in 
plan, draw a vertical line at each end, completing the front and the side 
of the building; from the point g on the perspective in plan, draw a per- 
pendicular to the perspective, measure the height of the hip roof on the 
corner of the building, draw a line from this point to V, intersecting this 
perpendicular line in the perspective, from this point draw a line to V, 
this is the ridge of the roof in perspective; project perpendicularly the 
point h and i to the perspective, that intersect the line g to V, draw lines 
to intersect with points, that will form the hip roof in perspective. The 
block perspective is now complete, the method of drawing the other motives 
in perspective, that compose the architectural design, will be a repetition 
of the method as described. 

The delineation of the perspective in plan of edifices, in which the 
roof is broken up into gables, forming valleys at their point of intersection 
with the body of the roof, hip roofs and the roofs of projecting wings, 
forming angles at forty-five degrees with the horizontal, and projecting 
bay windows, the point of intersection should be located and drawn in 
the perspective in plan, by the measuring point X, continued until they 
intersect with a line that forms a part of the plan that they are to become 
a part of. 

In the various illustrations the position of C has been marked, as it 
is the line on which the vertical heights are to be put into scale measure- 
ments, regardless of where this position is located ; it is always moved on 
a horizontal line representing the picture plane, a group of objects can 
be located in front of this plane or in back of it. Plates Nos. 33 to £0, 
inclusive. 

When necessary the right and the left hand vanishing points can be 
set in one-half inch from the edge of the drawing board. This difference 
in the diameter of the semi-circle need not be taken into consideration, as 
it will not affect the perspective in any manner. 

Cities in which the streets do not run at right angles to each other, 
as in some instances for the sake of variety streets and avenues are intro- 
duced into the layout that run diagonally through the city or branch off 
from one of the main arteries at different angles. At the intersection of 
streets running at right angles, or at opposite angles to thoroughfares of 
this character, plots of ground of very irregular form are to be had, and 
are sometimes used for building sites. The common forms are a one-half 
of a regular polygon, triangular or a trapazeum; however, these plots of 

35 



Perspective Delineation 

ground are usually left open and given some landscape treatment, and 
called a Plaza or Square in commemoration of some Patriot, or otherwise 
named. When plots of ground of this character are to be used for building 
sites and the edifice is to be drawn in perspective, it often presents a per- 
plexing problem for the delineator. Four examples of this type of per- 
spectives are illustrated on Plates Nos. 21 and 22. We have to first con- 
sider that the orthographic plan of the edifice can be enclosed by a rect- 
angle, or a square, as it has been derived from this geometrical figure, with 
parts added to or cut away from it. After the angle of view has been 
chosen, then the perspective in plan can be drawn and the vanishing points 
for the oblique angles found. The length of the two sides of the edifice, 
as enclosed in a geometrical figure, of a rectangle or a square, should be 
laid off on the measuring line from A to B and B to C, also that portion of 
the edifice that is cut off by the intersection. The length of the sides in the 
orthographic plan are to be laid off on the measuring line and projected 
to the sides of the rectangle or square drawn in perspective in plan, by 
the measuring points, then to the vanishing points ; from a to a' by M', and 
from f to f by M, thereby locating the two points on the rectangle a' and f ' ; 
in this instance it is the front of the building, in which the diverging 
horizontal lines of the other two sides of the edifice in perspective, will 
be connected by the parallel horizontal lines of this elevation. Measure off 
the length of one side of the edifice on the measuring line a to b, by the 
measuring point M', locate b' on the rectangle, or the line drawn from 
B to V, draw a line from b' to V. The distance from f to g is the length of 
the base of a right-angled triangle, or that portion of the edifice that is cut 
off of the rectangle or square in the orthographic plan of the edifice, 
this distance to be measured on the measuring line f to g and projected 
from these points to the rectangle by the measuring point M, locating g 7 , 
from g' draw a line to intersect the line from b' to V, locating the point c, 
this gives the length of one side of the edifice in perspective in plan ; a line 
drawn from d to d' by M' to intersect the line BV at d' and continued to 
the vanishing point V will locate e, at the point of intersection with the 
line h'V. The distance from f to h is the length of the other side of the 
edifice measured on the measuring line, h is projected to BV by M and 
then to V, intersecting the line drawn from d' to V locating the point e, 
this gives the length of the two sides of the edifice in perspective in plan, 
a line drawn from a' to c and extended to the picture plane, also one drawn 
from f to e and extended to the picture plane will locate the vanishing 
points V ' ' and V" which are the vanishing points for the two sides of 
the edifice in perspective in plan; this completes the perspective in plan 
of the edifice. The vanishing points obtained in the manner described 
above are to be used for the delineation of the perspective in plan only, 
as V and V are the vanishing points for the perspective. 

36 



The Principles of Perspective 

THE theoretical analysis of the primary principles of perspective are 
of little value unless they are considered from a broader point of 
view, as the problems given in an academic course are of such minor 
nature and are so largely surrounded by theoretical limitations that it re- 
duces the student's point of view to the narrowest margin. It leaves him 
drifting about in a sea of uncertainty, with little that is other than 
theoretical to rely upon when he attempts to apply what he has been taught 
to practical problems in perspective delineation, he is unable to produce 
credible results. Eventually he follows the same path that others have trod 
before him and enters that class of delineators who render perspectives 
by their own chosen methods, relying somewhat on good judgment, and 
what seems fairly correct perspective, or those who delineate perspectives 
without adhering to its established principles; as they are able to judge 
from the appearance of the finished work, what is fairly correct per- 
spective. They maintain an uncertain attitude with regard to what they 
have produced. I guess that is about correct perspective. 

The final definition for the theoretical analysis of the primary prin- 
ciples of perspective is to be found in trigonometrical demonstrations. 
That branch of mathematics that treats of the relation of the sides and 
angles of triangles with methods of deducing from certain given parts 
other parts required. 

To illustrate how these trigonometrical principles are applied to 
theoretical perspective, we shall first consider the semi-circle which is 
divided into one hundred and eighty degrees or parts and each of these 
parts or points on its circumference to be a station point, from which an 
object is to be viewed. Considering that we will use fifteen of these di- 
visions as station points, starting with ten degrees on the left hand side, 
and advancing to eighty degrees on the right hand side of the center line 
of the semi-circle, at each of these station points we would obtain a differ- 
ent view of the object, the viewpoint at eighty degrees will be the reverse of 
that at ten degrees, Plate No. 2k. When the point of view is changed in this 
manner the distance the station point is from the picture plane increases 
up to the point of view at forty-five degrees and in turn diminishes as we 
approach the point of view at eighty degrees ; as we move in a radial line 
from the center of the semi-circle, which in turn will react on our view of 
the object; as we approach the object we will see less of its height, on 
account of the angle subtended by the point of view. 

The basic principles of this method are that all angles inscribed in a 
semi-circle are right angles, and that any right-angled triangle, which the 
dimension of one side is given, the length of the other two sides can be 
obtained by calculation, Plates Nos. 18 and 23. By assuming the distance 
the station point is from the picture plane to be one hundred and sixty-six 

37 



Perspective Delineation 

feet, and the angle of view is thirty and sixty degrees, this dimension will 
be the base of a right-angled triangle, which we will call a, the length of 
b and c are to be obtained by calculation. The length of the line b will be 
measured from the point of intersection of the orthographic plan, with 
the picture plane, to the vanishing point V, its length will be, as the 
length of a is multiplied by the cotangent of the angle of view (b — a x cot. 
A) or 166 x 1.73205 = 288; the length of the line c is to be measured 
from S or station point to V then c = /a2 + b2 or /166 s + 288* = 332.5 ; 
this calculation is for a semi-circle four feet in diameter, and an angle of 
thirty and sixty degrees, the perspective is to be drawn to the scale of 
one-eighth of an inch to the foot. Therefore M V is equal to S V and V S 
is equal to V M' by this method, these positions are obtained by trigo- 
nometrical calculation, for the angles of view from ten degrees to eighty 
degrees, advancing by five degrees', and are given in tabulated form under 
the headings, degree of angle on left and degree of angle on right; for 
the degrees of angles or points of view, and the positions on the picture 
plane, M C X and M', also the position of S or station point on the circum- 
ference of the semi-circle. The positions given in the tables on page 58 
are for a semi-circle one foot in diameter, the results obtained by multiply- 
ing these figures, for an angle of view, by the diameter of the semi-circle, 
will be in feet and decimals of a foot, and are to be laid off on the drawing 
with a scale or ruler; the distance from the picture plane to the station 
point should be multiplied by the scale used to actual size and laid off on 
the drawing, according to the scale that is being used for the perspective. 
By this method of calculation, the theoretical principles of perspective are 
crystalized into concrete form, and are applicable to all forms of perspec- 
tive delineation. 

Heretofore we have considered perspectives that would be classed as 
small, medium sized and large perspectives, or those that could be drawn 
on a drawing board of average size, and pointed out briefly that it was 
unnecessary to go beyond the limits of a drawing board, to place the 
vanishing and measuring points, for perspectives in which their height 
did not greatly exceed their length. We shall now consider perspectives 
that will require drawing boards of greater dimensions, for drawing 
bird's-eye view perspectives, or a view taken from an aeroplane, in which 
the viewpoint is to be taken above the surface of the earth, so that a group 
of objects can be seen in their entirety, from an elevated point of view. 
Delineators are often called upon to draw perspectives that cover large 
areas of ground, such as the development of an estate for an institution, 
or for an owner of an estate, the campus of a university showing its 
extent and the proposed buildings to be erected in the future. Perspec- 
tives of this character are somewhat different from the average, as the 
delineator is not concentrating his attention on any one object, but on 
numerous objects, assembled in a composite group, mingled with planted 

38 



Perspective Delineation 

areas and the undulating contours of the landscape, all the objects will 
appear slightly depressed, on account of the foreshortening in height, as 
well as in the other two dimensions. The delineator should exercise care 
in the execution and not attempt to draw objects in the picture that are 
directly below his point of view, or those that will not come within the 
confines of the focal angle. The assumed position of the picture plane 
should be located about the center of the group, so that the objects in the 
distant foreground that are a unit of the group will not be obliterated by 
the aerial perspective that performs a very important function in per- 
spectives of this character. 

To obtain a comprehensive idea of the group in its entirety, a pre- 
liminary drawing or a small scale study should be first made before the 
final drawing is started on a larger scale. This will enable the delineator 
to consider the group of the motives, the point of view and numerous 
other items that did not manifest themselves when first considered. This 
sketch need not be worked out in detail, or made into a finished drawing, 
as it is only for a preliminary study and a record for the delineator, to 
show that the work was started, should it be decided that the development 
was not to be carried out. 

A conservative estimate of the prevailing conditions will guide the de- 
lineator in his preliminary undertakings, first considering the height of 
the eye above the surface of the earth, the distance he can see on the sur- 
face of the earth from an elevated position, and what will come within 
the confines of the focal angle. The height the observed is above the 
earth's plane should be given careful consideration, as the hazy appearance 
of objects, due to their aerial perspective, is a very important item and 
should be treated with some consideration as to its presence; it is quite 
essential that the horizon appears in the picture as it should not convey 
a false impression in the mind of the casual observer, to whom the picture 
is to make a just appeal. The distance the eye can see on the surface of 
the earth, from that height, will by calculation give the distance it will 
be between the vanishing points. 

The Focal Angle 

Assuming that the focal angle of persons with normal vision is thirty 
degrees to the plane of the horizon, that is, the rays of light re- 
flected from objects are received by the eye at an angle of sixty 
degrees, measuring in a horizontal and vertical plane, thirty degrees above 
the horizon and thirty degrees below the horizon, and in a direct line 
toward the object, to the left and the right of the observer's point of view. 
Plate No. 25. Using the focal angle as a basis, all the points used for the 
delineation of the perspectives by the perspective in plan method can be 
obtained by calculation. Although it will only be necessary to resort to 
this method of calculation for very large perspectives, or perspectives of 

39 



Perspective Delineation 

edifices in which their height greatly exceeds the other two dimensions, 
such as perspectives of multi-storied buildings and bird's-eye view per- 
spectives. 

To illustrate more clearly what is meant by this statement, though 
there are no fixed rules that can be abided by, leaving it to the better 
judgment of the delineator to decide on what will be the best solution for 
the problem in hand. The distance the observer is from the object and 
the angle from which the edifice is to be viewed has a relative bearing 
on a distant point to which all horizontal lines appear to converge; the 
position of this convergence point is to the station point of the observer 
as the square root of (a a plus b 2 ). Therefore if a line were drawn from 
the station point of the observer to the object and its length ascertained, 
which we will call a, the distance the convergence point is from the point 
of intersection of this line with the object will be as a is multiplied by the 
cotangent of the angle of view. Plate No. 23. The application of these 
formulas for locating the vanishing points and measuring points to the 
problem at hand will give the diameter of a semi-circle, which will be the 
distance between the vanishing points V and V, and other preparations 
can be made accordingly for starting work on the perspective. 

When the height of the edifice above the horizon is over one hundred 
and eighty feet from a normal focal point of view on the earth's plane, 
the diameter of the semi-circle for a perspective of an edifice of this height 
will exceed seven feet, and the distance to the station point will be greater 
than three hundred feet. Considering that the scale used for the per- 
spective is one-eighth of an inch to the foot, then it will be necessary to 
calculate the distance to the station point by the cotangent of the focal 
angle ; if it is desired to view the edifice from a normal focal point, so as 
not to have it appear like a photograph taken with a wide angle lense, or 
the point of view taken at some height above the surface of the earth. 
Plates Nos. 27 and 28. 

To illustrate this method of calculation for obtaining the distance it 
will be from the picture plane to the station point for a perspective of a 
multi-storied building, the observer is to see the edifice in its entirety from 
a normal focal point of view; that is, the full height of the edifice shall 
come within the confines of focal angle. Plate No. 26. The method for 
obtaining the distance to the station point of the observer from the picture 
plane is the same as that used for obtaining the distance it will be to the 
vanishing point, that is out in space, from the position C, or the point of 
intersection of the orthographic plan with the picture plane; in this in- 
stance it applies to the vertical height of the edifice, and is to be measured 
on a horizontal plane to the station point; after obtaining the distance 
to the station point, then this measurement can be used for obtaining the 
distance it will be to the vanishing points that are out in space by the 
same method. Plate No. 26. 

40 



Perspective Delineation 

Assuming the height of the edifice to be five hundred and five feet 
above the ground line, and five feet from the ground line to the horizon, 
which is to be deducted from the height of the edifice for the purpose of 
calculating the distance to the station point. 

The point of view of the edifice is to be thirty and sixty degrees, to 
obtain the distance it will be to the station point, will be as the height of 
the edifice above the horizon is multiplied by the cotangent of the angle 
of view (b = a cot. A) or 500 x 1.73205 = 866.25, which is the distance 
in feet from the station point to the picture plane. To obtain the distance 
it will be from C on the picture plane to V, will be 866.25 x 1.73205 = 1500 
feet, the distance from V to C on the picture plane for the left hand vanish- 
ing point, for an angle of sixty degrees will be 866.25 x .57735 = 500 feet 
nearly, this gives the distance it will be from the point of intersection of 
the orthographic plan with the picture plane, to the left and to the right 
hand vanishing points, and the station point in feet, they are to be laid 
off on the drawing with a scale, the positions of the measuring points can 
be obtained, either by calculation or by the method described. In this 
instance both of the vanishing points will be off the average drawing 
board and the perspective will have to be drawn the long way of the 
board. It then becomes necessary to use the cardboard curves as men- 
tioned heretofore for drawing the perspective. For the figures used in 
making these calculations, by the cotangent of the angle of view, for ob- 
taining the positions used in the delineation of the perspective in plan 
method, the reader is referred to F. E. Kidders, Architects and Builders 
Pocket Book. 

Distortion in perspective delineation is often due to the fact that the 
station point is taken too near the edifice, as it is then viewed at too narrow 
an angle, to see the edifice in its entirety, the delineator is attempting to 
draw that which he cannot see from a normal point of vision, and the 
edifice may appear as though it spread out at the top. As the observer 
approaches the edifice, the upper stories will disappear from view. If the 
head is thrown back in order to see the upper portions, the lower portions 
of the edifice cannot be seen from this point of station, the focal angle 
would not be normal to the horizon. The station point should be taken at 
a sufficient distance from the edifice, so that the edifice can be seen in its 
entirety, when the focal angle is normal to the plane of the horizon. 

Designing in Perspective 

Designing in perspective has not become universal among architects, 
as it is usually considered that perspective is a work of special 
character. Generally the Architect's geometrical drawings are 
submitted to the client for approval after the plans have been accepted and 
a perspective is demanded. An extra compensation is charged for this 
service as it is let out to delineators that specialize in this line of endeavor. 

41 



Perspective Delineation 

In some instances, where designing in perspective is practiced in the offices 
of Architects, a perspective is submitted with the sketch plans. As this 
practice is so varied it is difficult to say to what extent designing in per- 
spective is practiced by Architects. 

Designing an edifice in perspective is in reality a simpler method of 
designing than designing the geometrical elevations separate ; the necessity 
of rearranging the motives on one elevation to conform with those on the 
other elevations will be avoided. The designer is considering the arrange- 
ment of the motives on two elevations, and has a broader aspect of the 
whole situation, as it can be readily seen how the proposed edifice will enter 
into and become a part of the accessories. 

Delineators who wish to dispense with matters of calculation and ob- 
tain the position of the measuring points without making a preliminary 
calculation for a sketch perspective; perchance they would have some 
reason to doubt the results obtained in this manner, on Plate No. 81 are 
nine perspective scales, for angles of view from ten degrees to eighty 
degrees, giving the position of the vanishing points and the measuring 
points for a semi-circle one foot in diameter, according to the figures given 
in the tables under the heading M, C, X, M'. By using the dividers, to 
take off the distance from the center line of the semi-circle, to the left or 
to the right, of this point as it happens to be and multiplying this measure- 
ment by the number of times it is to be enlarged, according to the number 
of times the full length of the scale will divide the length of the line drawn 
between the established vanishing points. These scales should facilitate 
matters to a limited extent on work in perspective delineation. If greater 
accuracy is desired the measurements taken with the dividers can be 
applied to the scale below for actual measurement. 

The orthographic plan of the average edifice, unless it is polygonal 
or triangular in form, is a rectangle, or a close approach to a square, as 
the length of one side is usually greater than that of the other ; but the long 
side need not be the more important facade, in which case the edifice will 
have to be viewed from a different angle of view. On Plate No. 32 are 
nine views of a cube, drawn at angles of view, from ten degrees on the 
left hand side, to eighty degrees on the right hand side, of the center line 
of the semi-circle; illustrating how an object with two equal faces, will 
appear in perspective from nine different points of view. By comparing 
the form of the orthographic plan to that of a square, and the perspective 
to that of a cube, it can be readily ascertained from the various views of 
the cube what will be a desirable point of view for the perspective that is 
to be drawn. 

Take for instance an edifice that is rectangular in plan, having the 
dimensions of one hundred and fifty feet frontage on an important street, 
and forty feet frontage on a street of lesser importance. The front on the 
important street should show in perspective a near approach to a full view, 

42 



Perspective Delineation 

and the narrower front allowed to vanish rather rapidly, and angle of 
view of about twenty-seventy would be preferable. Should the narrow 
front be the important facade, then the long side should be permitted to 
vanish rapidly, and near approach to a full view of this facade should be 
obtained, the angle of view for this perspective should be about forty-fifty 
or twenty-five - sixty-five. Should the orthographic plan be a rectangle, 
and the plot of ground an inside lot, with one important facade on the 
street front, this should be shown in a perspective full view, and the long 
side on the party wall line, allowed to vanish rapidly, an angle of view of 
ten-eighty would give the most desirable point of view. Should the ortho- 
graphic plan be close approach to that of a square, with two facades of 
equal importance, then we should consider the edifice as a cubical block. 
A good view of the edifice can be had at an angle of view of forty-five, 
forty-five, but this would allow all the returning mouldings, in the cornice 
and belt courses, to mitre in a straight line, without a profile to the mould- 
ings, at the corner of the edifice, if the intersection is a right angle and is 
not rounded off or ornamented; though this is not detrimental, and per- 
haps would not be noticed, if it were not called to attention ; however, this 
sort of thing can be obviated, the returning moulding given the desired 
profile, by taking the angle of view at twenty-five, sixty-five or forty-fifty. 
By comparing the form of the orthographic plan to that of a square, and 
then considering it in perspective as a cubical mass, it can be readily seen 
from the different views of the cube, on this plate, what will be a desirable 
view for the perspective of the edifice. 

Perspectives of an interior should be considered from a different view- 
point than that of an exterior. A perspective of the exterior of an edifice 
conveys an impression to the mind that something is advancing toward 
the observer or is drawn out for his inspection ; whereas that of an interior 
gives the opposite impression to that of an exterior view. The objects in 
a room appear as though they were moving toward a point farthest from 
the eye, wherein the greater length of the room will appreciably increase 
this aspect and can be compared to a view looking down a street. The 
buildings paralleling the sides of the street are the side walls, the street 
paving, the floor of the room and the open sky representing the ceiling, we 
then have a view of a room with an indefinite length. 

Perspectives of interiors are usually drawn in parallel perspective. 
However, a perspective drawn of an interior by this method and compared 
to a photograph taken from the same point of view would never appear 
quite the same, as the photograph would show a convergence to the parallel 
lines, on the three sides of the room, whereas an interior drawn in parallel 
perspective, the far end of the room would be a rectangle in which the 
vertical lines intersected with the horizontal at right angles ; as in angular 
perspective, the points of intersection are at oblique angles. A comparison 
of the two methods of perspective delineation for interior perspectives is 

43 



Perspective Delineation 

given on Plates Nos. 6 and 7. On Plate No. 33 is illustrated the same 
method for the delineation of an interior perspective as for that of an 
exterior. Plate No. 32. Taking a rectangular room as a basis, with the 
plane of the picture crossing the center of the room, a view showing the 
three walls of the room would be drawn at an angle of view of ten-eighty ; 
a room of which two walls are shown in the perspective, and one has an 
important motive, or wall decoration, that will be seen in the perspective, 
a better view of this motive can be had by changing the angle of view, say 
thirty-sixty, or if on the other side of the center line of the semi-circle, an 
angle of view of sixty-thirty. If one corner of the room is all that is to 
be shown in an interior perspective, and both walls have equally important 
wall decorations, a view at an angle of forty-fifty, or forty-five - forty-five 
will give the view desired. 



Picturesque Perspective 



THE accompanying sketch block perspectives illustrate to what extent 
the principles of perspective can be utilized in the delineation of pic- 
turesque groups of buildings. Heretofore we have considered the 
perspective of an edifice which is treated as an individual unit, with its 
accessories, and not as a group collectively. A large proportion of the 
delineators commissions will be of that nature, except when a bird's-eye 
perspective of a group of buildings is to be used collectively, but erected as 
individual units, on a large plot of ground. For the most part these block 
perspectives, are accompanied by a perspective in plan, of the group drawn 
to a smaller scale to show the method of arriving at these results. 

The relative importance attached to the position "C", which is in a 
direct line with the station point, and about which the picture plane is 
rotated should not be considered as a coincidence, as a step forward or 
backward, to the left or to the right, would change the point of view in 
its entirety. 

The first sketch on Plate No. 33 shows a building erected on an 
irregular plot of ground, formed by the intersection of two streets, and 
terminating in a plaza. The important facade fronts on the plaza, the 
horizontal lines in the composition of the motives, on this facade, having 
no vanishing point, but connect the ends of the termination horizontal 
lines, in the composition of the motives, on the two other facades. This 
sketch is drawn at an angle of forty-five degrees, and is accompanied by 
a perspective in plan on Plate No. 34. Compare with the sketches on Plates 
Nos. 21 and 22. 

A rise or drop in the grade line of a city street where the buildings 
rise perpendicularly on the building line, these different levels will often 
present a confusing problem to the delineator, when it is to be shown in 
perspective. The drop in the street grade, in the second sketch on 
Plate No. 33, is twelve feet, in one hundred and thirty-six feet, this depth 

44 



Perspective Delineation 

should be measured below the starting point, and projected to an estab- 
lished point on the edifice. The vanishing point for all lines that parallel 
this drop in the street grade, is found by measuring down in a vertical 
line, on the line representing the position C, the depth below the grade, 
and at the point of intersection of a line, drawn from this point, to a 
point, in the street below, then continued to the vanishing points; a line 
drawn from C on the sidewalk level to intersect the point just found, 
and continued to a line drawn through the plane of the vanishing point, 
will establish the vanishing point, for all lines that parallel this drop in 
the street grade. 

With reference to what has been said heretofore, regarding the point 
of view, in the third sketch on Plate No. 33 is a row of buildings ; fronting 
on an open space, drawn at an angle of view of twenty-five, sixty-five, 
as compared with a similar group on Plate No. 39, drawn at an angle of 
forty-fifty. The first mentioned sketch drawn at an angle of twenty-five, 
sixty-five, gives a view that contains little of interest, as it apparently has 
no stopping place, and the eye wanders along from one to another, finding 
nothing of interest until they vanish at infinity on the horizon. As in the 
second mentioned sketch, each member of the group attracts the attention, 
on account of their individuality, and pronounced character. In all per- 
spective delineation, the point of view should be considered of paramount 
importance, as on it depends whether the attention is to be concentrated, 
on a group of motives of particular interest, or is to be led away from 
the picture by the flow of line, that makes up the composition of the group. 

The possibility of taking advantage of the natural topography, in 
cities that are built on the sides of terraced hills, this sketch furnishes a 
good example of what will be often met with in perspective delineation. 
The stepped ramp rising above the street level, to the elevated terrace, 
allowing the lower portion of the building to be used for quarters and 
shops, with appartments above them. The method of obtaining the posi- 
tion of the vanishing points, for the parallel lines in the stepped ramp, 
and those that parallel the slope in the grade, are illustrated in the first 
sketch on Plate No. 35. 

This street scene, portrays a rather unusual subject to be delineated 
in perspective, scences of this character are usually drawn by parallel 
perspective, in this instance the angle of view is ten-eighty, giving a view 
of both sides of the street. The converging lines in the composition of 
the edifices, on the left and right hand sides of the street, pass beyond the 
plane of the vanishing point, and continue to rise until they pass beyond 
the plane of the picture. This is not a coincidence, as it will be apparent 
in all scenes of this character, in which some part of the assembled group, 
lies in front of the picture plane, and another portion in back of it, which 
forms the termination of the street, (compare this with the street scene 
Plate No. 8, in which the street is crossed by an elevated railway) and 

45 



Perspective Delineation 

the parallel horizontal lines converging to a vanishing point. The position 
of C is located in the center of the lamp-post, as shown by the perspective 
in plan on Plate No. 36. 

Methods of drawing arches and vaulting in perspective, are usually 
illustrated by orthographic projection, although a mechanical process, it 
is perhaps the best method of drawing them, if absolute accuracy is 
desired ; on the other hand, they appear about right, when drawn freehand, 
as the mechanically drawn arch, would not harmonize with the freeness 
of the surroundings. A series of arches around a court yard, are illustrated 
in the third sketch on Plate No. 35 drawn in angular perspective. 

The irregular plan of the dwellings and the garden wall, with the 
sidewalk following the contour of the canal, in the first sketch on Plate 
No. 37, requires locating a series of varnishing points, in a vertical plane, 
above and below the horizon, for the delineation of this sketch in perspec- 
tive. The sketch is drawn at an angle of twenty-seven degrees, owing to 
the large number of obtuse angles, in the irregular planning, it requires 
a vanishing point, for each system of parallel lines in the perspective in 
plan, as well as in the perspective. Although there was no real necessity, 
for this method of delineation, as with a few exceptions, all the obtuse 
angles could have been drawn as right-angles, and this alteration would 
not be perceptible, in the picture; but to be exact, and to follow out the 
true form of the irregular plan, the position of the various vanishing 
points were found, for the perspective in plan and for the perspective. 

A group in which each unit will hold the attention for a period of 
time, is illustrated in the second sketch on Plate No. 37 as the units are 
considered individually, there will always be something in reserve to 
attract the attention. The thoroughfare leading out of the picture, does 
not carry with it the point of interest, as it is interrupted at the junction 
point of the two streets, and the eye will always follow the triangular 
course, bringing it back to the starting point. This sketch is drawn at an 
angle of forty-fifty degrees, with a perspective in plan on Plate No. 38 
showing the position of C. 

In the third sketch on Plate No. 37 there can be no obvious reason 
given for this method of delineation, other than that, it was an attempt 
to produce a perspective, that would apparently be distorted from this 
point of view; in this sketch the remote corner of the building being 
farthest from the eye, and in a direct line with the station point, is drawn 
as though it was closest to the eye, allowing the picture plane to cut 
through the edifice back of the facade, that is to be delineated in perspec- 
tive; requiring the projection of all points, laid off on the measuring line, 
to the picture plane lying in front of this line, instead of back of it, 
as in the usual method of delineation. In reality the opposite corner of 
the edifice farthest from the corner on which the vertical heights are laid 
off to scale measurements, and the diverging parallel lines in the motives 

46 



Perspective Delineation 

to this point, would be rather diffused, as they pass beyond the plane of 
vision, if they were drawn as they would appear in actual projection, and 
not altered somewhat, they would be slightly distorted. As in this instance, 
the height of the edifice is about equal to that of a two story building, 
so the distorted form of the motives, was easily remedied ; however in an 
edifice of greater height, it is hardly possible that it could be as easily 
corrected, therefore this method of perspective delineation is not to be 
recommended. 

The first illustration on Plate No. 39 shows a group of buildings in 
block perspective, erected on the side and top of a low spreading hill, 
bordering on a small river. The view is drawn at an angle of twenty-five, 
sixty-five degrees, showing the position of the horizon and the ground 
line. The station point, is in a direct line with the position C, and the 
intersecting part of the sketch, lies back of the bridge spanning the river, 
with the picture plane cutting diagonally through this bridge. 

The average person viewing an object, or group of objects, the level 
of their eye would be from four feet, six inches to five feet, above the 
earth's plane which will be the horizon line. The delineator should be 
consistent in placing the height of the horizon above the earth's plane, 
and take in consideration the height of the eye of the average person, so 
as not to place it at a level from which the least number of persons will 
view the object. 

The second illustration on this page, shows a group of buildings 
sketched in block perspective, paralleling a street with the horizon line 
about the level of the eye of the average individual, which is the opposite 
to that of third illustration on this plate, in which the observer is at a 
height above the earth's plane. Delineators are often given a commission 
to draw a perspective of this character, in which a group of buildings 
are spread over a large area, and one of the buildings will be of greater 
importance than the others. In order to see those of lesser importance 
in the background, as they are a unit of the whole group, the viewpoint 
is taken above the center of the whole group, at one corner of one of the 
more important buildings. The elevated position from which this group 
is viewed, should not be confused with what has been said, regarding the 
viewpoint of the average person, in this instance it is a conception of 
mass, to the extent it is proposed to erect additional buildings, to the 
group, in the near future, showing the various units spread over a large 
area. 

Orthographic projection in perspective delineation is analogous to the 
surveying an irregular plot of ground, on the completion of the survey, 
by the surveyer, his line of traverse must close within a reasonable distance, 
without too great an allowance for the technical term "A personal Equa- 
tion." The motive selected for illustrating the method of orthographic 
projection, in perspective delineation, is drawn on Plate No. UO taken from 

47 



Perspective Delineation 

a perspective of the Masonic Temple, of Omaha, Neb., G. B. Prinz, 
Architect. It is essential, that accuracy should be the primary considera- 
tion in all orthographic projection, in the delineation of perspectives, as 
a very small margin is allowed the delineator, for looseness in his methods. 
To disregard this feature, the delineator will often experience considerable 
difficulty, in bringing the lines representing the returning mouldings, to 
close at the mitre points, without resorting to unnecessary work that 
would have otherwise been avoided. 

The relative position of the minor motives, entering into the composi- 
tion of this motive, with their relation to the building or property, as 
shown on this plate, are as follows : Taking the wall surface, around the 
openings as a basis, which is one foot and eleven inches from the building 
line, the face of the impost pilaster, is one foot and seven inches, from the 
building line, and the face of the large pilaster is eleven inches from the 
building line. The greater projection of the main cornice, is four feet 
beyond the face of the large pilaster. With these measurements as a basis, 
and measuring their height from an established point, and projecting the 
same to a line representing the center line of the large pilaster, in the 
plane of the building line, projecting the same point, back again to the 
center line of the large pilaster, it will give the required point in projec- 
tion. The same method of projection, is used to obtain the profiles of the 
mouldings, in the main cornice and the other motives as illustrated on 
this plate. 



48 



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